Yes, private colleges accept need-based scholarships and grants. Each school's financial procedure is slightly different, so if you aren't sure how scholarships work for a specific school, reach out to their financial office. Generally, need-based scholarships are accepted at all schools. Additionally, private schools tend to offer many scholarships to help their students pay for college attendance. Do some research on the schools you are interested in, but continue applying for scholarships, because there is a high chance any financial aid you receive will be accepted.