Ball-batting is a challenging task because it requires excellent eye-hand coordination and instantaneous decision making. Moreover, as a winning strategy, the task of ball-batting concerns not only about "hitting a flying ball with a bat", but about "sending the rebounding ball to a prespecified location". Therefore, the decisions on when and where to hit the ball and what the velocity of the bat is at the impact time are crucial for a successful ball-batting. Making such decisions should consider the flying and rebounding behavior of the ball and is very complicated. In this paper, we apply the deep reinforcement learning (DRL) method to train the ball-batting robot developed by the authors for making timely and appropriate batting decisions. A simulated environment consisting of a physical flying model and a neural network rebounding model is constructed for efficient training. Then experiments in the real world are conducted and the results show that after being trained by DRL, the robot can hit the incoming ball in all tests and send the rebounding ball to the target location with a successful rate of 58.8%.