Crystal structures were investigated for (001)-oriented tetragonal L1(0)-ordered MnGa epitaxial films with thicknesses of 1-30 nm grown at room temperature on the (001) surface of a CoGa B2-ordered alloy template with magnetron sputtering. All the films showed well-defined remanent magnetization with the magnetic easy axis normal to the film plane at zero magnetic field. The out-of-plane X-ray diffraction results showed that the tetragonal lattice gradually compressed along the [ 001] direction as the film thickness decreased. The reflective high-energy electron diffraction (RHEED) results showed that a morphology for the MnGa thin films became rougher with increasing thickness. The in-plane lattices showed tensile strain in the 1- to 3-nm-thick films, which gradually relaxed to the bulk value with increasing thickness. These results suggested pseudomorphic-like growth of MnGa films on CoGa at the heterointerface of gallides with a lattice mismatch of about -4%. The physics of this growth mode was discussed in terms of Co-Ga-Mn bonding at the heterointerface.