The exact solution is obtained for Green's function of an infinitesimal horizontal electric dipole on a dielectric slab backed by a ground plane of carbon fiber composite (CFC) material. We consider both reinforced continuous carbon fiber (RCCF) CFC and carbon nanotube (CNT) CFC. RCCF is modeled by an electrically anisotropic surface impedance tensor whereas CNT is modeled as isotropic. The spectral domain method is used and the asymptotic part of the integrand is treated by adding and subtracting that for a perfect electric conductor ground, leaving a rapidly-converging term for numerical integration. Numerical results based on this method compare well with results based on a time-domain finite integration technique. The effect of conductivity and anisotropy of the composite ground plane on electric field is investigated.