We propose a biomimetic approach for steering motion control of a snake robot. Inspired by a vertebrate biological motor system paradigm, a hierarchical control scheme is adopted. In the control scheme, an artificial central pattern generator (CPG) is employed to generate serpentine locomotion in the robot. This generator outputs the coordinated desired joint angle commands to each lower-level effector controller, while the locomotion can be controlled through CPG modulation by a higher-level motion controller. The motion controller consists of a cerebellar model articulation controller (CMAC) and a proportional-derivative (PD) controller. Because of the fast learning ability of the CMAC, the proposed motion controller can drive the robot to track the desired orientation and adapt to unexpected perturbations. The PD controller is employed to expedite the convergence speed of the motion controller. Finally, both numerical studies and experiments proved that the proposed approach can help the snake robot achieve good tracking performance and adaptability in a varying environment.