Based on the sliding mode control method, a new third-order fixed time convergent sliding mode nonlinear extended state observer (SMNESO) is designed to address the problems of slow tracking speed and low tracking accuracy of the traditional extended state observer for system states, and its convergence time and steady-state errors are analyzed. Firstly, a new fixed-time convergence sliding mode surface and sliding mode approach law are proposed, and a SMNESO is designed by the sliding mode control method. Secondly, it is proved that the SMNESO can achieve fixed-time convergence by the Lyapunov function, and the estimation error of the system disturbances is analyzed. Finally, the comparative simulation experiments show that the SMNESO can track the system states quickly and accurately, which has a significant performance advantage over the traditional extended state observer.