<p>To expand the use of robots to assist and replace workers in tasks, the robot needs to deal with not only repetitive and simple tasks but also complex and delicate tasks with high speed and high accuracy. In recent years, imitation learning has been used in several studies to enable robots to learn complex human-like motion with little learning cost. However, in the imitation learning framework, it is difficult to make teaching data that takes into account optimal acceleration/deceleration, force, and constraints of the robot from a control perspective. In this paper, we propose a control scheme to track a fast and smooth imitation motion by implementing a model predictive control (MPC) scheme. To accelerate and smooth human teaching motions, we designed an MPC that follows a reference trajectory output from a motion generator learned by using deep predictive learning (DPL). By adopting this approach, it is possible to suppress excessive accelerations and decelerations while maintaining the ability to follow the target imitation motion. This allows for an increase in the robot’s motion speed while preserving the task success rate. Through simulations of an object grasping task and actual environments of a door-opening task, we evaluated the effectiveness of the proposed control scheme.</p>