In this paper a control design of a nonholonomic mobile robot with a differential drive is presented. On the basis of robot kinematics equations a robot control is designed where the robot is controlled to follow the arbitrary path reference with a predefined velocity profile. The designed control algorithm proved stable and robust to the errors in robot initial positions, to input and output noises and to other disturbances. The obtained control law is demonstrated on a simple trajectory example, however, for a more general applicability a time-optimal motion planning algorithm considering acceleration constraints is presented as well