In recent years, uncooled infrared focal plane arrays (IRFPAs) have gained importance in the field of industrial gas leak detection; however, their applications often require the inclusion of narrow-band filters in the infrared objective lenses to limit the range of incident radiation, which, in turn, produces fixed-pattern noise that affects imaging quality. To this end, this study investigates the fixed-pattern noise model of uncooled IRFPA imaging considering the influence of filters and adopts the theory of the radiation conversion angle coefficient to establish a model of the fixed-pattern noise distribution formed by the filter’s, reflected, and stray radiations from the optical path environment on the IRFPA surface. Theoretical analysis and test results demonstrate that both results are basically consistent. Notably, the results of this study have a guiding meaning for the gas leak uncooled infrared imaging detection system for targeted non-uniformity correction, and have application value for improving the detection efficiency of the detection system.