Aiming at the problems of sudden changes in the acceleration rate and unsmooth control instructions of the time elastic band (TEB) algorithm in complex environments, an improved TEB algorithm was proposed. Firstly, this algorithm introduced the jerk constraint on the basis of the original TEB algorithm to smooth the velocity and acceleration curves and avoid oscillation and jitter phenomena of the robot during the movement process. Secondly, the method of adaptively adjusting the number of elastic band nodes was adopted to adaptively adjust the interpolation points, which improved the safety and stability of the robot’s movement process. To verify the effectiveness of the improved TEB algorithm, simulation and comparative experiments of the APF algorithm, DWA algorithm, traditional TEB algorithm and improved TEB algorithm were conducted in a long-distance long narrow corridor environment and a multi-turn environment including reverse parking. The results demonstrated that the improved TEB algorithm generated smoother paths. In corridor environments, the variance of linear velocity, the mean angular velocity, and the variance of angular velocity were reduced by 16.67%, 7.38%, and 12.84%, respectively, compared with the traditional TEB algorithm. In multi-turn environments, the corresponding reductions were 8.61%, 4.34%, and 8.58%, respectively. This led to smoother linear and angular velocities with reduced oscillations. Furthermore, the effectiveness of the algorithm has been validated in a real-world experimental environment.