In the event of a significant natural disaster or a local conflict, the demand for a regional satellite navigation becomes imperative. The navigation can provide accurate position information and navigation augmentation services for regional emergency operations. To satisfy the requirements, a formation configuration of low-Earth orbit (LEO) regional navigation satellites is proposed innovatively. The strategy of fly-around formation consisting of four satellites for LEO regional navigation is determined and a comprehensive configuration design method for the formation is presented, encompassing the determination of configuration parameters, the establishment of dynamic equations and the presentation of performance indicators, including duration of ground coverage, positioning accuracy Geometric Dilution Precision (GDOP) and fuel consumption. The effects of formation radius and orbit altitude on the performance indicators are analyzed, respectively. Based on the above investigations, a method to enhance regional navigation performances by using genetic algorithm (GA) guided by penalty function is introduced. The rationality and feasibility of the formation configuration are verified through simulation studies.