The passive infrared remote sensing system for gas detection has the advantages of low costs, small volume, and easy expansion. Due to signal drift and background noise interference in passive infrared gas detection based on narrow-band pass filters, it is necessary to modulate, filter and phase-lock the signal. In addition, the measurement signal received by the system is greatly by photochopper radiation, so we should establish a radiation model for the measurement process. In light of this, we investigated a radiation model for passive infrared detection based on a lock-in amplifier in this paper and proposed a signal processing method with phase judgment after the lock-in amplifier. Furthermore, we designed and built a passive multispectral system for gas detection, which was calibrated in the laboratory, and we also carried out blackbody measurements at different temperatures. The results show that the measured radiance on each channel is consistent with that from the established model. This study provides a model basis and experimental verification for passive infrared signals based on lock-in amplifiers, as well as a reference for the development of portable remote sensing systems for gas detection in a short range.