A near-infrared single-photon detection system is established by using pigtailed InGaAs/InP avalanche photodiodes. With a 50GHz digital sampling oscilloscope, the function and process of gated-mode (Geiger-mode) single-photon detection are intuitionally demonstrated for the first time. The performance of the detector as a gated-mode single-photon counter at wavelengths of 1310 and 1550nm is investigated. At the operation temperature of 203K,a quantum efficiency of 52% with a dark count probability per gate of 2. 4 * 10~(-3), and a gate pulse repetition rate of 50kHz are obtained at 1550nm. The corresponding parameters are 43% , 8. 5 * 10~(-3), and 200kHz at 238K.