A wide-band high-resolution echelle grating spectrometer is designed on the basis of an off-axis three-mirror reflective optical system and a multi-column linear array detector in this paper. First, the structural parameters of the echelle gratings are optimized with the instrument performance indicators as constraints so that the gratings can fold and overlap the wide working band within a small spectral order while ensuring high dispersion. The multi-column linear array detector is used for signal acquisition. Then, for the aberration correction of the wide free spectral region with high dispersion, the off-axis three-mirror reflective optical system is used as the focusing mirror and the off-axis parabolic mirror is used as the collimating mirror. The working band of the designed echelle grating spectrometer is 400--900 nm, and the F number is 4.5. The spectral resolution is 0.003, 0.004, and 0.005 nm at 402.31, 541.82, and 870.48 nm, respectively, and the system volume is 380 mm×325 mm×230 mm.