Infrared sky background level is an important parameter of infrared astronomy observations from the ground, particularly for a candidate site of an infrared capable observatory since low background level is required for such a site. The Chinese astronomical community is looking for a suitable site for a future 12 m telescope, which is designed for working in both optical and infrared wavelengths. However, none of the proposed sites has been tested for infrared observations. Nevertheless, infrared sky background measurements are also important during the design of infrared observing instruments. Based on the requirement, in order to supplement the current site survey data and guide the design of future infrared instruments, a multiband near-infrared sky brightness monitor (MNISBM) based on an InSb sensor is designed in this paper. The MNISBM consists of an optical system, mechanical structure and control system, detector and cooler, high gain readout electronics, and operational software. It is completed and tested in the laboratory. The results show that the sensitivity of the MNISBM meets the requirements of the measurement of near-infrared sky background level of several well-known astronomical infrared observing sites.