With the development of Internet of Things technology, the will to make cities smarter is growing. In the context of smart cities, where people are surrounded by a tremendous number of points of interests (POIs), POI recommendation is of great significance. The massive amount of user check-in data collected by location-based social networks (LBSNs) can help users explore new places via POI recommendations. With rich auxiliary data becomeing available in LBSNs, purely exploiting users' check-in information for POI recommendation is not sufficient. Although several attempts have been done to employ geographical influence to enhance POI recommendation, they simply use a certain distribution function to measure the geographical influence between POIs, which may lead to biased results. To this end, this article proposes a geography-aware inductive matrix completion (GAIMC) approach for personalized POI recommendation. Specifically, the GAIMC model consists of two parts, including geographic feature extraction via a Gaussian mixture model (GMM) and inductive matrix completion for recommendation. The GAIMC model first captures the geographical influence among users and POIs by the GMM, which can mine clustering information with hierarchical structures based on the users' check-in data and POIs' location information. Then, a matrix-completion method called inductive matrix completion, which can incorporate geographical features with the user-POI association metric, is utilized to recommend POIs. The experimental results on two real-world LBSN data sets demonstrate that our proposed model can achieve the best recommendation performance in comparison with the state-of-the-art counterparts.