Will I be eligible to apply for H1B?

Hi,

I went to US in 2006 on F1 visa.But I came back to India within a month without beginning my MS programme.

Will I be eligible to apply for H1 B? or will my past be a hinderance for my application in future?

It should not impact your H1. During the interview the visa officer might ask you about your previous F1 visa and you need to answer truthfully to the best of your knowledge.