Complete the University of Houston application for admission using The Common Application. A certified bank letter, indicating that the sponsor is financially capable of meeting the student's education and living expenses, must be submitted.With a GPA of 3.5, University of Houston requires you to be around average in your high school class. You'll need a mix of A's and B's, and very few C's. SAT minimum score of 940 or ACT minimum score of 18. Click on Submit to submit your online application. There is also an appeals process students can go through. STEP 1: Create and submit application. Students seeking admission to the Graduate School of Texas Southern University should request and complete an application for graduate admission.