Actual debugging actions during the testing phase in the software development and the operation phase are not always performed perfectly. In other words, all detected software faults are not corrected and removed certainly. Generally, this is called imperfect debugging. In this paper, we discuss a software reliability growth model considering imperfect debugging that faults are not always corrected/removed when they are detected. Defining a random variable representing the cumulative number of faults corrected up to a specified testing time, this model is described by a semi-Markov process. We derive various quantitative measures for software reliability assessment and show their numercal examples.