This paper investigated mathematical modelling and control scheme of Static Synchronous Compensator (STATCOM) based on fuzzy logic controller. At first, based on switching functions, a mathematic model of STATCOM in the form of a matrix was presented. Then, to overcome the problem of lacking an accurate model of a power system with STATCOM, a fuzzy logic PI controller was established in the feedback loop circuit. The membership function of the fuzzy logic controller was gained through the collection of experimental data. The proposed control scheme and the mathematic model were validated by MATLAB simulation, which showed that STATCOM with the designed fuzzy logic controller was able to improve the transient stability and voltage stability of power systems effectively.