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A framework to generate a human-like arm motion of a humanoid robot using an Evolutionary Algorithm (EA)-based imitation learning is proposed. The framework consists of two processes, imitation learning of human arm motions and real-time generating of a human-like arm motion using the motion database evolved in the learning process. The imitation learning builds the database for the humanoid robot that is initially converted from human motion capture data and then evolved using a genetic operator based on a Principal Component Analysis (PCA) in an evolutionary algorithm. This evolution process also considers the minimizing of joint torques in the robot. The database is then used to generate humanoid robot's arm motions in real-time, which look like human's and require minimal torques. The framework is examined for humanoid robot to reach its arms for catching a ball. Additionally, the inverse kinematics problem to determine the final posture of 6-DOF robot arm with a waist for the task of catching a ball, is proposed.