The learning strategy in the canonical particle swarm optimization (PSO) algorithm is often blamed for being the primary reason for loss of diversity. Population diversity maintenance is crucial for preventing particles from being stuck into local optima. In this paper, we present an improved PSO algorithm with an interswarm interactive learning strategy (IILPSO) by overcoming the drawbacks of the canonical PSO algorithm's learning strategy. IILPSO is inspired by the phenomenon in human society that the interactive learning behavior takes place among different groups. Particles in IILPSO are divided into two swarms. The interswarm interactive learning (IIL) behavior is triggered when the best particle's fitness value of both the swarms does not improve for a certain number of iterations. According to the best particle's fitness value of each swarm, the softmax method and roulette method are used to determine the roles of the two swarms as the learning swarm and the learned swarm. In addition, the velocity mutation operator and global best vibration strategy are used to improve the algorithm's global search capability. The IIL strategy is applied to PSO with global star and local ring structures, which are termed as IILPSO-G and IILPSO-L algorithm, respectively. Numerical experiments are conducted to compare the proposed algorithms with eight popular PSO variants. From the experimental results, IILPSO demonstrates the good performance in terms of solution accuracy, convergence speed, and reliability. Finally, the variations of the population diversity in the entire search process provide an explanation why IILPSO performs effectively.