A software quality estimation model is often built using known software metrics and fault data obtained from program modules of previously developed releases or similar projects. Such a sup ervise dlearning approach to software quality estimation assumes that fault data is available for all the previously developed modules. Considering the various practical issues in software project development, fault data may not be available for all the software modules in the training data. More specifically, the available labeled training data is such that a supervised learning approach may not yield good software quality prediction. In contrast, a supervised classification scheme aided by unlabeled data. i.e., semi-supervised learning, may yield better results. This paper investigates semi-supervised learning with the Expectation Maximization (EM) algorithm for the software quality classification problem. Case studies of software measurement data obtained from two NASA software projects, JM1 and KC2, are used in our empirical investigation. A small portion of the JM1 dataset is randomly extracte dand used as the labeled data, while the remaining JM1 instances are used as unlabeled data. The performance of the semi-supervised classification models built using the EM algorithm is evaluated by using the KC2 project as a test dataset. It is shown that the EM-based semi-supervised learning scheme improves the predictive accuracy of the software quality classification models.