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In this paper, an efficient real-time autonomous driving motion planner with trajectory optimization is proposed. The planner first discretizes the plan space and searches for the best trajectory based on a set of cost functions. Then an iterative optimization is applied to both the path and speed of the resultant trajectory. The post-optimization is of low computational complexity and is able to converge to a higher-quality solution within a few iterations. Compared with the planner without optimization, this framework can reduce the planning time by 52% and improve the trajectory quality. The proposed motion planner is implemented and tested both in simulation and on a real autonomous vehicle in three different scenarios. Experiments show that the planner outputs high-quality trajectories and performs intelligent driving behaviors.