The basic theories of Particle Swarm Optimization (PSO) is introduced and illustrated with flowchart. In this study one of its improved algorithms Adaptive Particle Swarm Optimization (APSO) is introduced. Characteristics of basic PSO algorithms are outlined. Some methods of APSO at present were introduced and analyzed with their parameters. Limitation of these APSO algorithms was analyzed. Pointed out that APSO algorithms can be improved with adjustment of parameters and some other hybrid APSO are referred. Finally, pointed out application of PSO needs to be extended, hybrid with other algorithms is thought a good way to improve APSO algorithm and applying the improved algorithm to complex problems is the goal of our study.