The growth and saturation characteristics of an electromagnetic (EM) wave in a Smith-Purcell free-electron laser (FEL) with a Bragg cavity are investigated in detail with the aid of numerical simulation based upon the fluid model of the electron beam. To analyze the problem, a two-dimensional (2-D) model of the Smith-Purcell FEL is considered. The model consists of a planar relativistic electron beam and a parallel plate metallic waveguide, which has a uniform grating carved on one plate. For confinement and extraction of EM waves, a Bragg cavity is formed by a couple of reflector gratings with proper spatial period and length, which are connected at both ends of the waveguide. The results of numerical simulation show that a compact Smith-Purcell FEL can be realized by using a Bragg cavity composed of metallic gratings.