According to whether the systems vary over time, the decision systems can be divided into two categories: static decision systems and dynamic decision systems. Most existing feature selection work is done for the former, few work has been developed recently for the latter. To the best of our knowledge, when an object set varies dynamically in incomplete decision systems, no feature selection approach has been specially designed to select feature subset until now. In this regard, a feature selection algorithm based on compact discernibility matrix is developed. The compact discernibility matrix is firstly introduced, which not only avoids computing the time-consuming lower approximation, but also saves more storage space than classical discernibility matrix. Afterwards, we take the change of lower approximation as a springboard to incrementally update the compact discernibility matrix. On the basis of updated compact discernibility matrix, an efficient feature selection algorithm is provided to compute a new feature subset, instead of retaining the discernibility matrix from scratch to find a new feature subset. The efficiency and effectiveness of the proposed algorithm are demonstrated by the experimental results on different data sets.