Finite failure non-homogeneous Poisson process models proposed in the literature exhibit either constant, monotonic increasing or decreasing failure occurrence rates per fault and are inadequate to describe the failure process underlying both increasing/decreasing failure rates. In this article, we propose generalized inverse exponential software reliability growth model, which can capture both increasing/decreasing nature of failure occurrence rate per fault. The system parameters are estimated by means of the maximum likelihood estimators and the properties of the estimators are discussed. The experimental results of real data show that our proposed model performs better.