Many existing software reliability models (SRMs) are based on the assumption that fault correction activities take a negligible amount of time and resources, which is often invalid in real-life situations. Consequently, the estimated and predicted software reliability tends to be over-optimistic, which could in turn mislead management in related decision-makings. In this paper, we first make an in-depth analysis of real-life software testing process; then a Markovian SRM considering fault correction process is proposed. Parameter estimation method and software reliability prediction method are established. A numerical example is given which shows that by using the proposed model and methods, the results obtained tend to be more appropriate and realistic.