In software development life cycle, software testing is one of the most important tasks; and in the testing, software reliably is very important aspect for any category of software systems. A number of testing-effort functions for software reliability growth model based on non-homogeneous Poisson process (NHPP) have been proposed in the past. Although these models are quite helpful for software developers and have been widely accepted and applied in the industries and research centers, we still need to put more testing-effort functions into software reliability growth model for accuracy on estimate of the parameters. In this paper, we will consider the case where the time dependent behaviors of testingeffort expenditures are described by New Modified Weibull Distribution (NMWD). Software Reliability Growth Models (SRGM) based on the NHPP are developed which incorporates the (NMWD) testing-effort expenditure during the softwaretesting phase. It is assumed that the error detection rate to the amount of testing-effort spent during the testing phase is proportional to the current error content. Model parameters are estimated by Least Square and Maximum Likelihood estimation techniques, and software measures are investigated through numerical experiments on real data from various software projects. The evaluation results are analyzed and compared with other existing models to show that the proposed SRGM with (NMWD) testing-effort has a fairly better faults prediction capability and it depicts the real-life situation more faithfully. This model can be applied to a wide range of software system. In addition, the optimal release policy for this model, based on reliability criterion is discussed.