In this paper, we consider H-infinity control of linear and semilinear diffusion systems by using a finite-dimensional controller. The main aim is to construct a finite-dimensional stabilizing controller for the linear diffusion system that makes the H-infinity norm of the closed-loop transfer function less than a given positive number delta. For that purpose, we first derive a finite-dimensional reduced-order system for the linear diffusion system. Then, a stabilizing controller that makes the H-infinity norm of the closed-loop transfer function less than another positive number is constructed for the reduced-order model. It is proved that the finite-dimensional controller, together with a residual mode filter, plays a role of a finite-dimensional stabilizing controller that makes the H-infinity norm of the closed-loop transfer function less than delta for the original linear diffusion system if the order of residual mode filter is chosen sufficiently large. Moreover, it is shown that the finite-dimensional H-infinity controller constructed for the linear diffusion system also works as a finite-dimensional H-infinity controller for a semilinear diffusion system with sufficiently small nonlinear term.