This contribution presents a novel approach for nonlinear time-optimal model predictive control (MPC) based on Timed-Elastic-Bands (TEB). The TEB merges the states, control inputs and time intervals into a joint trajectory representation which enables planning of time-optimal trajectories in the context of model predictive control. Model predictive control integrates the planning of the optimal trajectory with state feedback in the control loop. The TEB approach formulates the fixed horizon optimal control problem for point-to-point transitions as a nonlinear program. The comparative analysis of the TEB approach with state-of-the-art approaches demonstrates its computational efficiency. The TEB approach generates a trajectory that approximates the analytical time-optimal trajectory in few iterations. This efficiency enables the refinement of the planned state and control sequence within the underlying closed-loop control during runtime.