Taking a dual-band spectrometer as an instance, a stray radiation suppression device was designed for a compound optical system which began with a Cassegrain structure. The device contains outer baffle 1,outer baffle 2 and two inner baffles, in which the baffle 2 efficiently blocks the external stray radiation directly into the optical system. The device can effectively suppress the stray radiation of each spectrum, and with this device, the difference between parasitic light and signal light in visible branch are 7~8 orders of magnitude, which in near infrared branch are 5~6 orders of magnitude. In practical, the device performs well as the image is not affected by the stray radiation, as well as, the working time can be enlarged.