Yeah, Drexel University does provide scholarships based on merit. Here are some of them:

Drexel Merit Scholarship
Total Worth: Varies, determined by the students’ credentials
Eligibility: Varies, determined by the students’ credentials
Requirement for maintenance: a 2.75 cumulative GPA and full-time status
Separate application needed: No

Drexel Global Scholar program
Total Worth: Full-tuition scholarship
Eligibility: Full-tuition scholarship
Requirement for maintenance: Full-time enrollment
Separate application needed: Yes
Application deadline: November 15 ( early decision) or February 1(Early Action and Regular Decision applicants)

Drexel University provides aids at an average of 42948 per student meeting 82% of students need. 100% of students with need receive financial aid at an average of 32749 need-based grant. They also provide other scholarships including Delaware Valley Science Fair Winners Scholarships and Eagles Fly for Leukemia Scholarship.