A dual-differential-driven mobile robot is consisted of two differential driving modules equipped with normal-shape wheels, suffering from constraints of nonholonomic and redundancy in motion. A two-input-two-output nonlinear kinematics model was established for path tracking of the proposed mobile robot and then linearized by the approach of input-output linearization. The need for coordinating the speeds of two driving modules was analyzed when considering the redundancy in motion, and a hybrid control law combining an evaluation function method of error intelligent-transformation with an approach of exponential stability control was proposed. The evaluation function method was used to compute the suitable control output intelligently for different error states so as to convert them into the applicable range of exponential stability control. Then the latter was used to eliminate posture angle error and distance error synchronously towards zero. The results of digital simulation and experiment test showed that the hybrid control law could transform error states smoothly and eliminate two pose errors synchronously, and the mobile robot could track the linear and circular guide paths accurately and steadily.