To improve the efficiency of port berth scheduling, and aiming at the shortages of grey wolf optimization with slow convergence speed and easy to fall into local optimum, an improved grey wolf optimization is proposed. The improved grey wolf optimization allocates the initial positions of individuals by sin chaotic sequence, enhancing the population uniformity and ergodicity. The head wolf leading strategy is introduced to accelerate the convergence of the algorithm and improve the efficiency of the algorithm. The cooperative competition mechanism is introduced to enhance the local search ability of the algorithm. When the gray wolf population is updated, the adaptive weight is introduced to meet the optimization requirements of different periods. Finally, the performance of the algorithm is analyzed and compared with six algorithms. Experiments show that the algorithm has obvious advantages in convergence speed and convergence accuracy. And the standard deviation of the solution obtained by running the algorithm 20 times independently is 0, which shows that the algorithm has good immunity to solving problems of different dimensions. Besides, satisfactory results have been achieved in the application of port berth scheduling, after the optimization of the algorithm, the total stay time of all ships was reduced by 14.7% compared with before. So the algorithm can obtain relatively better scheduling schemes and provides a new strategy for port berth scheduling optimization.