Multi-site MIMO (Multiple Input Multiple Output) is a key technology to enable next generation cellular networks to achieve high throughput in the cell-edge areas. This paper presents a scheduling algorithm that can be applied to a multi-site MIMO cellular system. Our proposed scheduling scheme, named finite-automaton type scheduler (FA-scheduler), aims to achieve further improvement of cell-edge user throughput. The FA-scheduler is a simple scheme. Here we introduce one setting parameter for user throughput in order to prioritize user terminals whose throughput is lower than the setting parameter. The simulation results show that the user terminals whose user throughput is near the setting parameter are in the majority when the FA-scheduler is applied. The improvement of the cell-edge user throughput depends on the setting parameter.