Test case prioritization is an effective and practical technique in regression testing. It schedules test cases in order of precedence that increases their ability to meet some performance goals, such as code coverage, rate of fault detection. In previous work, the test case prioritization techniques and metrics usually assumed that testing requirement priorities and test case costs are uniform. In this paper, basing on varying testing requirement priorities and test case costs, we present a new, general test case prioritization technique and an associated metric. The case study illustrates that the rate of "units-of-testing-requirement-priority-satisfied- per-unit-test-case-cost" can be increased, and then the testing quality and customer satisfaction can be improved. Keywords: Software Testing, Regression Testing, Test Case Prioritization, Priority, Cost