Drug repositioning is critical to drug development. Previous drug repositioning methods mainly constructed drug-disease heterogeneous networks to extract drug-disease features. However, these methods faced difficulty when we are using structurally simple models to deal with complex heterogeneous networks. Therefore, in this study, the researchers introduced a drug repositioning method named DRDSA. The method utilizes a deep sparse autoencoder and integrates drug-disease similarities. First, the researchers constructed a drug-disease feature network by incorporating information from drug chemical structure, disease semantic data, and existing known drug-disease associations. Then, we learned the low-dimensional representation of the feature network using a deep sparse autoencoder. Finally, we utilized a deep neural network to make predictions on new drug-disease associations based on the feature representation. The experimental results show that our proposed method has achieved optimal results on all four benchmark datasets, especially on the CTD dataset where AUC and AUPR reached 0.9619 and 0.9676, respectively, outperforming other baseline methods. In the case study, the researchers predicted the top ten antiviral drugs for COVID-19. Remarkably, six out of these predictions were subsequently validated by other literature sources.