SUMMARY Fault zones often serve as the major fluid pathways in a variety of geo-energy systems, such as deep geothermal systems. However, injection-induced instability of faults can sometimes lead to large-magnitude earthquakes. Cyclic injection has thus been proposed as an alternative injection protocol to better manage and mitigate the associated seismic risks. The risks of injection-induced seismicity depend primarily on the extent and magnitude of the fluid pressure perturbation. When fluid is injected into a fault zone, the local fault permeability will be enhanced, which in turn promotes the migration of fluid along the fault. This nonlinear process is further complicated during cyclic injection via alternating the injection pressure. In this study, both numerical and analytical modelling are conducted to investigate cyclic fluid injection into a fault zone with pressure sensitive permeability, in which the local fault permeability changes as a function of the local effective stress. The match with laboratory-scale experimental and field-scale analytical results of cyclic fluid injection verifies the accuracy of the numerical model. The parametric study reveals that the injection pressure attenuation, quantified by the amplitude ratio and phase shift, is enhanced by a lower initial fault permeability, a smaller stress sensitivity coefficient and a shorter period of pressure cycle (i.e. a higher frequency). Besides, the amplitude of the pressure cycle has a negligible effect on the injection pressure attenuation. We also discuss the implications of our results for the less amenable far-field seismic hazard and post shut-in seismicity.