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In this paper, we present a logistic fault-dependent detection model where the dependent-rate of detected faults in the software can grow much faster from the beginning but grow slowly as the testing progresses until it reaches the maximum number of faults in the software. The explicit function of the expected number of software failures detected by time t, called mean value function, of the proposed model is derived. Model analysis is discussed based on normalized-rank Euclidean distance (RED) and other criteria to illustrate the goodness-of-fit criteria of proposed model and compare it to several existing NHPP models using a set of software failure data. The confidence interval for the parameter estimates of the proposed model is also presented. A numerical analysis based on a real data set of the 7 or higher magnitude earthquake in the United States to illustrate the goodness-of-fit of the proposed model and a recent logistic growth model is also discussed. The results show that the proposed model fit significantly better than all the existing software reliability growth models.