Abstract: CO2 laser pump source is one of the most important core components of optically pumped THz gas laser, and its performance will directly affect the stability of the THz laser. A blazed grating is generally employed as a total reflecting tail mirror to constitute a grating resonator. The intra-cavity beam modes in the grating resonator are numerically studied with the transit matrix eigenvector method in this paper. A series of eigenmodes and the corresponding diffraction losses are calculated. It is shown that the characteristics of the intra-cavity eigenmode in a grating resonator are equivalent to those of a plane-concave resonator. For the grating resonator with a large Fresnel number, the diffraction loss of the lowest order mode in the vicinity of the Littrow wavelength may be lower than that of the higher order modes at the Littrow wavelength. In that case, the discrimination of the output longitudinal mode becomes weak.