Objective Anticancer drug combination therapies are a promising therapeutic strategy. Drug combinations exhibiting a highly synergistic effect are crucial to improve the treatment for specific cancers. However, identifying such combinations is very complicated and difficult due to the tremendous screening cost. The availability of large-scale high-throughput combination screening data provides opportunities for computational approaches. The purpose of this study is to optimize the high-throughput virtual screening of anticancer drug combinations in a completely data-driven and computational modeling way, and provide theoretical reference for “old drugs repositioning as new combinations”.Methods Inspired by the matrix completion, we present a nuclear norm regularization-based model, termed NNRM, to predict synergy scores and synergy status of anticancer drug combinations. Symmetric observation matrixes of synergy scores were constructed for given cell lines; a folding technique was employed to sparse the observation matrix; alternating direction multiplier method and soft threshold estimation were applied to solve the model.Results NNRM achieved expected predictive result on the dataset released by O’Neil’s team, the root mean square error of the synergy score prediction was 14.78, and the accuracy of the synergy status prediction was 0.94. It is not only significantly superior to the Random Forest and the Support Vector Machine, but also completely comparable to the state-of-the-art deep learning models including DeepSynergy, Deep learning+PCA and AuDNNsynergy. Moreover, NNRM effectively filled the missing synergy scores most of which are consistent with existing research or clinical practice.Conclusion NNRM could predict the synergistic effect of large-scale drug combinations in batches, which greatly lowers the data requirements by existing models, reduces the computational cost, and shortens the screening time. It indicates that NNRM is an alternative tool for high-throughput virtual screening of anticancer drug combinations.