Regression testing, which can improve the quality of software systems, is a useful but time consuming method. Many techniques have been introduced to reduce the time cost of regression testing. Among these techniques, test case prioritization is an effective technique which can reduce the time cost by processing relatively more important test cases at an earlier stage. Previous works have demonstrated that some greedy algorithms are effective for regression test case prioritization. Those algorithms, however, have lower stability and scalability. For this reason, this paper proposes a new regression test case prioritization approach based on the improved Annealing-Genetic algorithm which incorporates Simulated Annealing algorithm and Genetic algorithm to explore a bigger potential solution space for the global optimum. Three Java programs and five C programs were employed to evaluate the performance of the new approach with five former approaches such as Greedy, Additional Greedy, GA, etc. The experimental results showed that the proposed approach has relatively better performance as well as higher stability and scalability than those former approaches.