Software reliability growth model is one of the fundamental techniques to assess software reliability quantitatively. A number of testing-effort functions for modeling software reliability based on the nonhomogeneous Poisson process (NHPP) have been proposed in the past decades. Although these models are quite helpful for the software testing, we still need to put more testing-effort into software reliability modeling. This paper develops a software reliability growth model based on the non-homogeneous Poisson process which incorporates the Burr Type III testing-effort. This scheme has a flexible structure and may cover many of the earlier results on software reliability growth modeling. Models parameters are estimated by the maximum likelihood estimation and the least square estimation methods, and software reliability measures are investigated through numerical experiments on actual data from three software projects. Results are compared with other existing models which reveal that the proposed software reliability growth model has a fairly better prediction capability and it depicts the real-life situation more faithfully. Also, these results can provide a flexible tool on the decision making for software engineers, software scientists, and software managers in the development company. Furthermore, the optimal software release policy for this model based on costreliability criteria has been discussed.