The original artificial fish swarm algorithm (AFSA) has weak global search ability and poor robustness and is easy to fall into local extremum. Given these problems, an adaptive and differential mutation artificial fish swarm algorithm (ADMAFSA) is proposed. Firstly, it utilizes an adaptive vision field and step length strategy to improve the fine search ability of individuals in better areas of the population and enhance the optimization accuracy of the algorithm. Secondly, to explore potential better areas, the opposition-based learning mechanism is introduced into the random behavior of artificial fish swarms. Thereby, the algorithm can get better global searching ability and avoid premature convergence. Finally, inspired by the differential evolution algorithm, a mutation operation is applied to poorly performing artificial fish to increase the diversity of the fish swarm and reduce the possibility of the algorithm falling into the local extremum. To validate the performance of the improved algorithm, the proposed algorithm is tested with six benchmark test functions and eight CEC2019 functions. The experimental results indicate that, compared to other AFSA variants and novel intelligent algorithms, ADMAFSA demonstrates improvements in terms of optimization accuracy and robustness. Furthermore, in designing the train of gears, the optimization effectiveness of the improved algorithm is further proved.