The reason I am suggesting you December is - 1.Under OPT you will have plenty of Time to search Job 2. Some employers might wanna observe you in probation period before applying for H1B 3. H1B starts on APril every year. There is no specific last month to apply. The application is open until quota is available. This year general quota was exhausted by May 26. 11,000 out of 20,000 is still available for Masters Degree Holder. Last year this masters Degree quota was exhausted only at the end of year, December. Make sure you have sufficent documentation to apply for Masters Quota immediate after graduation because as I know it takes considerable time to receive Diploma once you graduated. Whenever you apply, Good Luck