Multimodal optimization aims to find multiple global and local optima as opposed to only the best optimum. Parallel genetic algorithms (PGAs) provide a natural advantage for dealing with this issue, since they are multi-population based searching methodologies. For single population based evolutionary algorithms, a number of niching and multimodal optimization techniques have been proposed and successfully applied to cope with this problem. However, these approaches are definitely not applicable for PGAs, since due to communicational and computational costs it is very always impossible to obtain and compute global information of all the sub-populations during massive parallel evolution procedure. In this study, a new island model PGA, called local competition model (LCM), is developed to cope with this issue. The new method only uses local information received from a few neighbouring subpopulations to reach a global diversification in which all the subpopulations are automatically allocated to different areas of searching space so that they can converge to multiple optima including both global optima and local optima. Finally, experimental studies on both real number optimization and combinatorial optimization are implemented to illustrate the performance of the new PGA model.