In this paper, we investigate a Software Reliability Growth Model (SRGM) based on the Non Homogeneous Poisson Process (NHPP) which incorporates a logistic testing-effort function. Software reliability growth models proposed in the literature incorporate the amount of testing-effort spent on software testing which can be described by an Exponential curve, a Rayleigh curve, or a Weibull curve. However, it may not be reasonable to represent the consumption curve for testing-effort only by an Exponential, a Rayleigh or a Weibull curve in various software development environments. Therefore, we will show that a logistic testing-effort function can be expressed as a software development/test effort curve and give a reasonable predictive capability for the real failure data. Parameters are estimated and experiments on three actual test/debug data sets are illustrated. The results show that the software reliability growth model with logistic testing-effort function can estimate the number of initial faults better than the model with Weibull-type consumption curve. In addition, the optimal release policy of this model based on cost-reliability criterion is discussed.