Software testing is required to detect the faults and to ensure the quality of the software under development. Usually, test suites are used to evaluate the software system during the software development cycle. But often test suites contain more redundant test cases due to overlapped test objectives. So, the test-suite reduction is an important step to reduce the number of test cases so as to satisfy the entire objectives with less computational cost. Literature presents different methods to select the suitable test suites of optimal subsets for regression testing. Accordingly, this research aims to develop an effective test suite reduction approach for regression testing. The proposed algorithm (GTAP) is newly designed using TAP measure and greedy search algorithm. This algorithm uses TAP-measure which is specially developed for measuring the importance of test cases. The performance of the GTAP algorithm is evaluated using four different evaluation metrics with eleven subject programs available in SIR repository. From the experimentation, the average performance of the proposed GTAP algorithm in all the programs is 93.07% which is higher than the DIV-GA which obtained the value of 90.27%.