In this paper, we show that graphene-coated nanowire integrated with a semi-elliptical dielectric substrate could enable excellent subwavelength transmission performance in the mid-infrared range. The fundamental graphene plasmon mode behaviors on the thickness of silica layer, ratio of long- to short-axis of the ellipse, nanowire radius, and chemical potential of graphene are revealed in detail. By improving the geometric parameters and the surface conductivity of graphene, results show that deep-subwavelength modal field size and long propagation could be achieved. Our findings may promote the applications of graphene-coated nanowires in tunable nanoscale photonic devices and sensors.