How could I solve this situation in a professional way?

I have a difficult sitaution at work. I am feeling discrminated. This started when I joined my work as a temporary staff with a male colleague. This male was given better training and was entitled to more tasks than I although we had the same job description. When I discussed this with my boss, he said that he prefers a male for these tasks. A year passed and I could prove efficiency. At the same time, the office needed to select regular staff among the temporary staff. Although we had a job interview and written exam, the management selected the most important person to the office and didn't much care for the exam and interview results. This person has become my boss as a result.

Although I proved efficiency, I still feel bad because of this unjustified descrminative situation. How could I put an end to that situation in a professional manner? I love my career and doesn't want to quit but I can see that this situation negativly affects my career development.

There is never an easy way to go about a problem like this. I would say all you really can do is continue to work hard and prove that you are a hard worker and efficient at what you do. That is the only way to really fix the problem you will never get upper management to change their minds by complaining. They will probably just see it as exactly that a complaint and label you. Do your best to work through it and not let it get to you. That's not to say in time, if the problem continues and you have done everything by th book, you couldn't present the issue again to your boss. I'm sure as long as it comes from your heart and you have already proven yourself not to be a complainer then your boss would definitely take your concern into consideration.

When you say work as "temporary staff", do you mean through a staffing company? If so, then you have no recourse. You were never an employee, and so the employment law stuff doesn't apply to you.

Find a job where they like you.

They are breaking the law
http://www.eeoc.gov/types/sex.html
Stand up for your rights and file a charge of employment discrimination. http://www.eeoc.gov/charge/overview_char...

your a temp, you got nothing, they could call your temp service tomorrow and say they do not want you anymore.

race/sex card won't work here

I am a white male and have been discriminated against in the work place for a number of reasons. Sometimes the guys who are most similar to the boss get close with the boss, Sometimes the boss percieves that you are not right for a certain job although you think you are. You need to stop feeling the victim. If you really want to stay at your current job you need to start outworking, out learning, and take on more responsibility than your coworkers. If you are truly by far the superior employee over time management will not be able to ignore it. Don't let missing your first chance at a promotion upset you. It usually takes many tries to get the position you want. Ask your boss (or your boss's boss) what you will need to do to be promoted. He may know some weakness you have that you are not aware of. Next chance at promotion you will have more experience. Or you will be qualified to get a similar job elsewhere.

Your story doesn't specify if you are employed by the company or a separate temp agency. I'm assuming you are an actual employee. Your supervisor crossed the line when he said that he "preferred a male" for those jobs. He showed personal preference based on gender, despite other traits the job required.
You have a case that your promotion was denied based on gender discrimination.
I don't believe they can fire you out of retaliation but I'd line up another job just in case you want to file a claim. There are people who file claims, win and stay and succeed at their jobs.

Unfortunately, if the promotion and hiring decisions are being made by the person who told you that he "preferred a male for these tasks" you may be fighting a battle that you can not win. It sounds like you will need to start looking for another job with another organization that is in need of someone with your background and skills. You other choice is to realize the limits that are there (due to that manager having those opinions) and either live with that or you need to find another job. Did you ask your boss why he prefers a male for these tasks? What tasks is it he is talking about?

You could file a claim of discrimination with the E.E.O.C. and wait for that process to conclude. That could take months, and even a year or so to go through (via appeals by both sides) and it will not be comfortable for you to continue working there while it's going on.