The path planning problem is of essential significance for the theoretical research and practical applications of mobile robot navigation. However, it is found to be non-deterministic polynomial time hard (NP-hard) problem. Aiming at solving the problem of the large computational complexity, an adaptive quantum evolutionary algorithm with improved population initialization, adaptive quantum gate operation, crossover and mutation is presented to better the computing performance. The experimental simulation results have demonstrated that the proposed algorithm has high speed of convergence and good global search capability and thus proved that our algorithm is effective and feasible for the trajectory planning of mobile robot in obstacles environments.