The transient photovoltaic responses in InAs/GaSb type-Ⅱ superlattice infrared photodetectors under picosecond pulsed laser illumination are reported. By analyzing the dynamic processes in the transient response curves of the p-b-i-n structured type-Ⅱ superlattice detectors, the apparent carrier lifetime can be obtained. A series of single element devices with different mesa areas have been investigated. The minority carrier lifetime trends to increase as the mesa area increases, implying a reduced surface recombination resulted from the un-passivated side-walls of the mesa. The investigated minority carriers are attributed to holes, with the apparent lifetime in the range 2-12ns.