A new modeling approach for the non-homogeneous Poisson processes (NHPPs) based software reliability modeling is proposed to describe the stochastic behavior of software fault-detection processes, of which the failure rate is not monotonic. The fundamental idea is to apply the Marshall-Olkin distribution to the software fault-detection time distribution. The applicability of Marshall-Olkin distribution in software reliability modeling is studied. The data fitting abilities of the proposed NHPP-based software reliability model is compared with the existing typical ones through real software project data analysis.