Intuitive joystick-based mobile robot operations are critical in terms of work efficiency in tasks where humans and robots work closely, such as in smart factories or electric wheelchairs. An operator-centric joystick mapping algorithm, based on a questionnaire study of 101 respondents, was proposed to determine the expected movement direction of a differential drive robot according to the joystick direction of the operator. The proposed approach considers the kinematic constraints of differential drive robots and maps the operator’s joystick control input to the robot velocity command by efficiently conveying the intention of the operator. This method generates a smooth robot velocity command from the continuous movement of the joystick without a sudden change in acceleration. The proposed algorithm was evaluated by 22 test subjects maneuvering a two-dimensional joystick module to control a virtual robot in a simulated environment visiting waypoints, and demonstrated superior performance when compared with two standard algorithms. The proposed algorithm was also implemented as a hardware system with a physical differential drive robot for testing in a real environment.