Taking the signal processing unit of an IR searching system as a pulse receiver, and considering the effect of bandwidth of the pulse receiver on the output signal-to-noise ratio, the range equation of IR searching system is derived. According to the condition in which the pulse receiver will give the optimum output signal-to-noise ratio, the dependence of bandwidth of the Signal processing unit on the dwell time of the detector is determined, and the corresponding range equation is obtained, thus providing the guidelines for designing and evaluating the performances of the IR searching system.