This work is to study the effect of doping concentration in the active layer on the performance of multiple quantum well (MQW) infrared photodetector based on inter sub-band transitions. A theoretical model for the photocurrent and hence, responsivity of the detector in frequency domain is developed considering the effect of doping dependent absorption and carrier capture at the hetero-interfaces. Transit time and capture time limited bandwidth of the detector is computed from the frequency dependent photocurrent. Results show that, besides the usual effect of capture time, doping concentration in the active layer has an important effect on the bandwidth and responsivity of the device particularly for high value of capture time.