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We proposed a new learning algorithm, named Geometric Reinforcement Learning (GRL), for path planning of Unmanned Aerial Vehicles (UAVs). The contributions of GRL are as: (1) GRL exploits a specific reward matrix, which is simple and efficient for path planning of multiple UAVs. The candidate points are selected from the region along the Geometric path from the current point to the target point. (2) The convergence of calculating the reward matrix is theoretically proven, and the path in terms of path length and risk measure can be calculated. (3) In GRL, the reward matrix is adaptively updated based on the Geometric distance and risk information shared by other UAVs. Extensive experimental results validate the effectiveness and feasibility of GRL on the navigation of UAVs.