Good community health service can offer residents healthcare and disease prevention. For the super residential communities surrounding the city, the population is huge and it is essential to build equivalent number of community hospitals. The reasonable site location facilitates residents' lives and achieves the most benefits with the least construction cost. It is necessary for the site selection of public facility to take fairness and benefits into account together. Therefore, a gravity model based on piecewise linear utility is presented to achieve the maximized utility of the system. Lagrangian relaxation algorithm, simplifying the solution process, is employed to obtain the results. Then, the proposed methodology is explained and the related issues are discussed with a case study in Huilongguan Community. The results indicate that the attraction of a community hospital is a crucial aspect besides the distance.