Synergistic drug combinations can improve the therapeutic effect and reduce the drug dosage to avoid toxicity. In previous years, an in vitro approach was utilized to screen synergistic drug combinations. However, the in vitro method is time-consuming and expensive. With the rapid growth of high-throughput data, computational methods are becoming efficient tools to predict potential synergistic drug combinations. Considering the limitations of the previous computational methods, we developed a new model named Siamese Network and Random Matrix Projection for AntiCancer Drug Combination prediction (SNRMPACDC). Firstly, the Siamese convolutional network and random matrix projection were used to process the features of the two drugs into drug combination features. Then, the features of the cancer cell line were processed through the convolutional network. Finally, the processed features were integrated and input into the multi-layer perceptron network to get the predicted score. Compared with the traditional method of splicing drug features into drug combination features, SNRMPACDC improved the interpretability of drug combination features to a certain extent. In addition, the introduction of convolutional networks can better extract the potential information in the features. SNRMPACDC achieved the root mean-squared error of 15.01 and the Pearson correlation coefficient of 0.75 in 5-fold cross-validation of regression prediction for response data. In addition, SNRMPACDC achieved the AUC of 0.91 ± 0.03 and the AUPR of 0.62 ± 0.05 in 5-fold cross-validation of classification prediction of synergistic or not. These results are almost better than all the previous models. SNRMPACDC would be an effective approach to infer potential anticancer synergistic drug combinations.