This paper proposes a task decomposition and dedicated reward-system-based reinforcement learning algorithm for the Pick-and-Place task, which is one of the high-level tasks of robot manipulators. The proposed method decomposes the Pick-and-Place task into three subtasks: two reaching tasks and one grasping task. One of the two reaching tasks is approaching the object, and the other is reaching the place position. These two reaching tasks are carried out using each optimal policy of the agents which are trained using Soft Actor-Critic (SAC). Different from the two reaching tasks, the grasping is implemented via simple logic which is easily designable but may result in improper gripping. To assist the grasping task properly, a dedicated reward system for approaching the object is designed through using individual axis-based weights. To verify the validity of the proposed method, wecarry out various experiments in the MuJoCo physics engine with the Robosuite framework. According to the simulation results of four trials, the robot manipulator picked up and released the object in the goal position with an average success rate of 93.2%.