The point-of-interest （POI） recommendation services provided by the location-based social network （LBSN） have become an important means of mining users' preference for POIs. The sparsity of user-POI matrix is the primary problem to be solved， and a large number of unknown values in implicit feedback cannot reflect user preferences. To improve recommendation precision， this paper proposes a point of interest recommendation algorithm integrating social geographical information based on weighted matrix factorization （SGWMF）. The social information is modeled through the power-law distribution. The check-in information of the user's friends is converted into the user's visit location preference. Secondly， the power-law distribution of geographical information is used to construct the user's visit location preference matrix to alleviate the data sparsity problem. Thirdly， in order to extend the effectiveness of the model， we improve the objective function by adding implicit feedback term. Finally， the experimental results on two datasets show that it has better performance than other POI recommendation algorithms and can improve the accuracy of recommendation results.