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Traditional artificial fish swarm algorithm (AFSA) can be affected by visual field parameters, and the step size of the artificial fish also constrained the performance. The step size of the artificial fish is fixed and it can affect the global search speed of the algorithm. So, a kind of logarithmic function adaptive artificial fish swarm algorithm (ALF-AFSA) is proposed. Based on the weighted average distance of artificial fish swarm, the logarithmic function is used as the moving factor of the step size. Also, the algorithm is applied to the function optimization and TSP problem as well as the path planning problem of the mobile robot. Compared with the traditional artificial fish swarm algorithm and weighted average distance artificial fish swarm algorithm, simulation results show that the presented algorithm has relatively higher optimization ability, and the global search ability is much better.