Supervisor gave my PhD project to another student I am a PhD student in life sciences. My PhD project's goal is to analyze specific data and to check a totally new idea in the field I am working in. This project is risky, however, very promising. With my supervisor, we planned all the studies and experiments before the start of the PhD, and he did promise that this would be my project. However, just as I started the PhD, he asked me to finish other experiments as I am the only one in the department who knows methodology and that work was crucial for the lab funding.

At the same time, he gave my project to another student claiming that he wants to know results and to publish this as early as possible. This student started the experiments and to analyze data. Moreover, my supervisor presented him to our collaborator (well known and influential scientist in the field) as the main researcher. 

At this point I am desperate. Yes, I am jealous, but just don't know what to do in this situation. I came to this lab only for this project. I tried to mention this to my supervisor, but he just said: "Well, these findings are very important to us and I want to know the results as soon as possible".

It's only 4 months into experiments and I hope that someone could suggest how can I change this situation.
If this was really the way you were treated - by which I mean that you have to be sure not to misinterpret statements or promises of your supervisor - then you should run.

A PhD requires trust between the supervisor and the student. After such a breach of trust, you need to find a new supervisor.