The surface plasmon excitation spectrum is calculated for the semi-infinite 3D Dirac semimetal. We used the random phase approximation for the calculation of the surface dielectric function, from which we derived the dynamical structure factor. The surface excitation spectrum shows a well-defined strong surface plasmon peak due to the plasmon mode in the bulk, with a noticeable influence of electron-hole excitations at large wave vectors parallel to the surface. The obtained spectrum will be useful for experimentally exploring the surface spectral properties of 3D topological Dirac semimetals.