Incorporating tags into matrix factorization is a hot topic in the field of recommender system. Based on adaptive tag selection, we propose a new matrix factorization recommendation algorithm. Firstly, we put forward a tagrating sparsity factor, which balances the usage of latent factors and tags in recommendation. Secondly, tag vectors are computed by the number of tags, which reflects the influence of different frequencies of tags on different items. Finally, the overall description of the proposed algorithm is illustrated. Experimental results show that the proposed algorithm has high recommedation accuracy and high convergence speed.