Regression testing is an expensive testing procedure utilized to validate modified software. During regression testing, a modified system is retested using the existing test suite. Because the size of the test suite may be very large, testers are interested in detecting faults in the system as early as possible during the retesting process. Regression test selection techniques attempt to reduce the cost of regression testing by selecting a subset of a program¿s existing test suite. In this paper we have briefly discussed two of the selection techniques and choose the safe algorithm technique. The previous researches indicate that safe regression test selection can be cost-effective, but that its costs and benefits vary widely based on a number of factors. In order to carry through the regression testing quickly and effectively, we have proposed a regression testing approach from a large test suite using hybrid technique based on safe selection algorithm and prioritization based on cost criterion. We examined some prioritization strategies and develop our proposed algorithm to improve the rate of fault detection for web applications.