Is it possible for an Indian student with M.Sc degree to do M.S course in USA? I heard BS degree in USA is of 4 years, but in India MSc is done after BSc.
Honestly, it really depends on the University. Some universities do not allow you to do a masters in the same field, twice - for example : http://cs.stanford.edu/admissions/faq#a2
Some of them will waive GRE/GMAT scores if you hold a master's degree (couldnt' post the link here, apparently I need 10+ reputation to do this). Other universities are more interested in whether your graduate degree had a research/thesis component to it, or if it was just a course based masters, like the one from NorthEastern (CS dept), for example, where a thesis is optional.
For the most part, masters in science, AFAIK, are seldom course based, and more research oriented - so any university worth its soul will not want its students wasting time/resources on a second master's degree in the same subject - they encourage applicants to consider a PhD instead.
However, if you hold a master's degree in, say, Physics - and want to pursue graduate studies in computer science, this is usually okay.
Could you post details about which subject you've done your masters and bachelors in, whether your graduate degree was had a paper/thesis component, and what you want to pursue in the states? That may help narrow down the answer.
So long as you meet or exceed (but not by too much!) the graduate admission requirements of a department, there's no reason you shouldn't be able to study there. There's no fixed rule that says that you can't do a master's in India then do one in the US as well. (If there is such a rule, it applies only to the departments or universities that impose them; there are no universal rules that govern US graduate admissions.)
The best bet is, of course, to contact the schools you're interest in attending and ask them directly what their policies are.
Absolutely! M.Sc. from a recognized Indian university usually meet the admission requirements in the US. Except if you had a M.Sc degree from IISC, IISERs, IITs, NITs and a couple of good universities; I think its advantageous to apply for a MS in the US in the perspective of research experience. Else and if you wish to do a PhD in the US, better appear GRE.