Multi-joint snake robot is a vital reconnaissance, surveillance and attack weapon in national defence and military in the future. To study the trajectory tracking problem of a multi-joint snake robot with high redundancy and multi-degree of freedom in the plane, an adaptive trajectory tracking controller of a multi-joint snake robot considering non-holonomic constraints is proposed in this paper. The adaptive trajectory tracking controller replaces unknown parameters in the environment wi t h estimated values, which effectively solves the negative effects caused by uncertain and time-varying environmental parameters in the process of the robot movement and realizes the stability of the controller. Firstly, a new dynamical model of a multi-joint snake robot is established through coordinate transformation. Secondly, the control objective of the controller of the multi-joint snake robot is established. Thirdly, the proposed controller of the multi-joint snake robot is designed by the Backsteppi n g method to realize the control of the joint angle tracking error, link angle tracking error, actuator torque error and motion speed error of the robot. Then, a suitable Lyapunov function is found to verify the stability of the controller. Finally, through the MATLAB simulation and prototype experiment, the motion process of the multi-joint snake robot is observed, the trajectory tracking performance of the robot is analyzed, and the effectiveness of the adaptive trajectory tracking controller is verified.