The nonhomogeneous Poisson process (NHPP) model is an important class of software reliability models and is widely used in software reliability engineering. The failure intensity function is usually assumed to be continuous and smooth. However, in many realistic situations, the failure intensity may be not continuous for many possible causes, such as the change in running environment, testing strategy, or resource allocation. The change-point and other parameters are often unknown and to be estimated from the observed failure data. In this article we constructed a method of the type of maximum likelihood estimation, which can be applied in the case that the change-point is not necessarily the observation time point and in the case that the data is grouped. Furthermore, if the failure intensity function is completely unknown, we designed a nonparametric method for estimating the change-point.