Hi Varish, welcome to the Forum.
Isn't an F1 visa a Student visa, which allows you to come to the US to go to school?
If that's the case (which is what it says on Wikipedia) then no, when your schooling is over you would have to either get a new visa of the correct type to stay here as a legal worker, or return to your home country.
You probably need to talk to someone in your area that specializes in immigration and citizenship, so you can get proper legal advice on this.
Bob Parker
Complete Internet Consulting
http://en.wikipedia.org/wiki/F-1_visa
EmploymentExcept for on-campus employment of 20 hours a week or less, F-1
students are generally not permitted to work in the US without prior
authorization from Citizenship and Immigration Services (USCIS). However, the USCIS may grant work authorization for Curricular Practical Training (CPT) and Optional Practical Training
(OPT). Students are permitted to work for a total of 40 months towards
practical training (eg. internship), which can be distributed between Curricular Practical Training (CPT) and Optional Practical Training
(OPT). An interim order was passed on April 8, 2008 allowing students
in STEM (Science, Technology, Engineering and Mathematics) to legally
work under OPT for 29 months.
[1] During the period of OPT, a F-1 student is not permitted to accrue more than 90 days of unemployment.