The infrared sky brightness level is an important parameter for infrared astronomical observation from the ground. It is necessary to obtain the infrared sky brightness level at an observatory site to evaluate the feasibility of infrared telescopes and instruments. In order to evaluate the possibility of developing infrared astronomical observations at several sites in China, the design of a continuous-scanning near-infrared sky brightness monitor (CNISBM), measuring 2.5 to 5  μm infrared sky brightness based on an InSb detector and a linear variable filter, is proposed. The optics and the detector were put in a vacuumed cryogenic dewar to reduce the background emission. The CNISBM has been tested by measuring the flux intensity of the observing window in the L-band. The results show that the sensitivity of CNISBM satisfies the requirements of the observations of 2.5- to 5-μm near-infrared sky brightness.