Based on the generalized Snell's law, the relationship between the phase gradient of the metasurface and the incident frequency is demonstrated, and the principle of the achromatic metasurface is developed. By adjusting the phase gradient and linear dispersion simultaneously, the function of achromatic aberration is realized, and the influence of chromatic aberration on the metasurface is reduced. We propose a metasurface stealth device with achromatic multilayer frame metasurfaces with beam deflection, steering, and collection functions so that the incident electromagnetic beam is transmitted around the stealth object without scattering. In the range of 0.45-0.9 THz, the stealth function can be achieved. We have shown that the achromatic principle, design method, and stealth structure provide a guide for achieving transmissive cloaking.