Fluid-injection-induced seismicity often accompanies reactivation of natural fault systems which has become a major environmental problem in the fields of development of Enhanced Geothermal Systems, extraction of hydrocarbon in shale gas reservoirs, and waste water disposal. We present a numerical modelling and investigate how the seismicity induced by nearby high-rate fluid injection evolves depending on the effect of permeability contrast between the fault systems and the reservoir rock. Modelled magnitude of induced seismicity tends to be higher with presence of less permeable fault system than the reservoir rock.