In this paper, we propose a cost-aware Rapidly-exploring Random Tree (RRT) path planning algorithm for mobile robots. A mobile robot is presented with a cost map of the field of interest and assigned to move from one location to another. As a robot moves, the robot is penalized by the cost at its current location according to the cost map. The overall cost of the robot is determined by the trajectory of the robot. The goal of the proposed cost-aware RRT algorithm is to find a trajectory with the minimal cost. The cost map of the field can represent environmental parameters, such as temperature, humidity, chemical concentration, wireless signal strength, and stealthiness. For example, if the cost map represents packet drop rates at different locations, the minimum cost path between two locations is the path with the best possible communication, which is desirable when a robot operates under the environment with weak wireless signals. The proposed cost-aware RRT algorithm extends the basic RRT algorithm by considering the cost map when extending a motion segment. We show that the proposed algorithm gives an outstanding performance compared to the basic RRT method. We also demonstrate that the use of rejection sampling can give better results through extensive simulation.