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

Blanche E. Seaver Scholarship
Total Worth: $36,000 per year
Eligibility: $36,000 per year
Requirement for maintenance: 3.25 Pepperdine cumulative GPA
Separate application needed: No

Regents Scholarship
Total Worth: $30,000 per year
Eligibility: $30,000 per year
Requirement for maintenance: 3.25 Pepperdine cumulative GPA
Separate application needed: No

George Pepperdine Achievement award
Requirement for maintenance: Minimum 2.0 cumulative GPA and Satisfactory Academic Progress
Separate application needed: No

Pepperdine University provides aids at an average of 39938 per student meeting 74% of students need. 100% of students with need receive financial aid at an average of 37244 need-based grant. They also provide other scholarships including The Lydia Hayne Scholarship Fund and Diane and Guilford Glazer Scholarship.