Kali, yes. Even Private students are eligible for NEET  subjective to age and aggregate criteria. You should be 17 years atleast by December 31st of year of admission and you should have completed your 12th in Physics, Chemistry and Biology with a minimum aggregate of 50% in these 3 subjects. It is 50% for General Category, 45% for PWD and 40% for OBC,SC,ST. Look at the criteria:

• Indian Nationals, NRIs, PIOs, OCIs, and Foreign Nationals
• No upper age limit as of now. The Candidate should be at least 17 years by December 31st of 2020
• You should have completed your 10+2 with Physics, Chemistry and Biology as your Core Subjects.
• 50% Aggregate in Physics, Chemistry and Biology for General Category, 45% for PWD and 40% for OBC,SC,ST Candidates.
• NIOS and Private Candidates are also eligible