Computational drug repositioning aims to discover new therapeutic diseases for marketed drugs and has the advantages of low cost, short development cycle, and high controllability compared to traditional drug development. The matrix factorization model has become the cornerstone technique for computational drug repositioning due to its ease of implementation and excellent scalability. However, the matrix factorization model uses the inner product to represent the association between drugs and diseases, which is lacking in expressive ability. Moreover, the degree of similarity of drugs or diseases could not be implied on their respective latent factor vectors, which is not satisfy the common sense of drug discovery. Therefore, a neural metric factorization model (NMF) for computational drug repositioning is proposed in this work. We novelly consider the latent factor vector of drugs and diseases as a point in the high-dimensional coordinate system and propose a generalized Euclidean distance to represent the association between drugs and diseases to compensate for the shortcomings of the inner product. Furthermore, by embedding multiple drug (disease) metrics information into the encoding space of the latent factor vector, the information about the similarity between drugs (diseases) can be reflected in the distance between latent factor vectors. Finally, we conduct wide analysis experiments on two real datasets to demonstrate the effectiveness of the above improvement points and the superiority of the NMF model.