Under certain conditions, chaotic oscillations will appear in a power system, affecting the safe and stable operation of the power grid. The dynamic behavior of chaotic oscillation in the fourth-order model of power system is analyzed and a controller based on adaptive non-singular terminal sliding mode control is designed. To ensure that the system converges within a limited time and does not produce singularity problems, the chaotic oscillation phenomenon in the fourth-order power system is quickly eliminated. To solve the problem that the damping coefficient and mechanical power usually have uncertainty in the fourth-order power system model, adaptive control is used to estimate it. This enhances the practicability of the controller. Simulation results demonstrate the effectiveness of the controller. This work is supported by the National Natural Science Foundation of China (No. 61803233).