We report on a high bandwidth measurement of the transient intersubband photocurrent of a GaAs/AlGaAs multiple quantum-well infrared photodetector (QWIP). The photocurrent is excited via tunable subpicosecond infrared pulses. The response time of the detector has a full width at half-maximum of 18.5 ps and a rise time of 14.5 ps, which is limited by the electrical circuit. The decay time of the photocurrent response exhibits a significant dependence on the applied voltage, with increasing decay times for increasing bias voltages. From the experimental data, we conclude that the intrinsic response time of a QWIP is less than 7 ps. ©1997 American Institute of Physics.