Background In the process of drug development, computational drug repositioning is effective and resource-saving with regards to its important functions on identifying new drug-disease associations. Recent years have witnessed a great progression in the field of data mining with the advent of deep learning. An increasing number of deep learning-based techniques have been proposed to develop computational tools in bioinformatics. Methods Along this promising direction, we here propose a drug repositioning computational method combining the techniques of Sigmoid Kernel and Convolutional Neural Network (SKCNN) which is able to learn new features effectively representing drug-disease associations via its hidden layers. Specifically, we first construct similarity metric of drugs using drug sigmoid similarity and drug structural similarity, and that of disease using disease sigmoid similarity and disease semantic similarity. Based on the combined similarities of drugs and diseases, we then use SKCNN to learn hidden representations for each drug-disease pair whose labels are finally predicted by a classifier based on random forest. Results A series of experiments were implemented for performance evaluation and their results show that the proposed SKCNN improves the prediction accuracy compared with other state-of-the-art approaches. Case studies of two selected disease are also conducted through which we prove the superior performance of our method in terms of the actual discovery of potential drug indications. Conclusion The aim of this study was to establish an effective predictive model for finding new drug-disease associations. These experimental results show that SKCNN can effectively predict the association between drugs and diseases.