In this paper, we propose a new learning algorithm, named as the Cooperative and Geometric Learning Algorithm (CGLA), to solve problems of maneuverability, collision avoidance and information sharing in path planning for Unmanned Aerial Vehicles (UAVs). The contributions of CGLA are three folds: (1) CGLA is designed for path planning based on cooperation of multiple UAVs. Technically, CGLA exploits a new defined individual cost matrix, which leads to an efficient path planning algorithm for multiple UAVs. (2) The convergence of the proposed algorithm for calculating the cost matrix is proven theoretically, and the optimal path in terms of path length and risk measure from a starting point to a target point can be calculated in polynomial time. (3) In CGLA, the proposed individual weight matrix can be efficiently calculated and adaptively updated based on the geometric distance and risk information shared among UAVs. Finally, risk evaluation is introduced first time in this paper for UAV navigation and extensive computer simulation results validate the effectiveness and feasibility of CGLA for safe navigation of multiple UAVs. (C) 2014 Published by Elsevier Ltd.