The higher a social mission of computer systems becomes, the more important developing highly reliable computer softwares becomes. During the testing phase in the software development, a developed software is repeatedly tested with a lot of test cases to remove latent software errors. Using the observed test data, it is of great interest to evaluate reliability for the developed software. In this paper, we propose and investigate a software reliability growth model for software error detection phenomena in the software testing. The useful software reliability measures are derived from the model. Using the number of test runs as the unit of software error detection period, the model is described by a nonhomogeneous Poisson process in which the random variable is the cumulative number of software errors detected by the testing. The model proposed here considers that the testing efficiency is geometrically decreasing with the progress of software testing. We apply this model to a set of actual software error data and illustrate the statistical inferences based on a method of maximum likelihood. Finally, an optimum software release problem using software reliability index is discussed as a practical application of the model.