This paper presents a sheet of graphene-ribbon waveguide as a simple and ultra-compact splitter and filter in the mid-infrared waveband. The central wavelength of the graphene surface plasmons (GSPs) and the coupling intensity of this splitter can be tuned by changing the physical parameters, such as the chemical potential, the width of the waveguide, the gap between neighboring graphene ribbons, the refractive index of the substrate, the carrier relaxation time, etc. The effects of these parameters on GSP waves and beam-splitter specifications are numerically depicted based on the finite-difference time-domain method. This proposed structure can be used to construct an ultra-compact fast-tunable beam splitter, filter, modulator, and switch in the mid-infrared range.