Pell Grant Modernization Act This bill amends the Higher Education Act of 1965 to modify eligibility requirements under the Federal Pell Grant Program. Specifically, the bill reduces the numbers of semesters a student is eligible to receive Pell Grants from 12 semesters to 10 semesters. In addition, the bill increases the number of credits students must take each semester in order to be considered a full-time student.