Drug repositioning serves as a promising strategy in drug development, exploring the potential uses of existing drugs through numerical computation. Compared to experimental screening, drug repositioning proves to be more efficient and cost-effective, playing a vital role in the field of pharmaceutical development. Designing an effective approach to integrate multi-source prior information about drugs and diseases holds significance in drug repositioning, given the low coupling of latent features in existing methods for handling the associated information and multi-similarity information of drugs and diseases. In this article, we propose a novel method based on multi-similarity geometric matrix factorization (multiGMF) for identifying the potential indications of existing and new drugs. Through weighted k-nearest neighbors (WKNN) algorithm and soft regularization technique, it couples the multi-similarity features of drugs and diseases with associated features. Moreover, it explores their latent feature information in high-dimensional space using graph regularization technique aimed at inferring potential drug-disease associations. To evaluate the performance of multiGMF, we contrast it with five most advanced drug repositioning approaches in both $10$-fold cross-validation and cold-start tests. The numerical outcomes demonstrate that multiGMF exhibits outstanding predictive performance. Furthermore, case studies further support the viability of our method in practical applications. The multiGMF code is freely available at https://github.com/YangPhD84/multiGMF.