We present an active quenching application-specific integrated circuit (ASIC), for use in conjunction with InGaAs-InP avalanche photodiodes (APDs), for 1550-nm single-photon detection. To evaluate its performance, we first compare its operation with that of standard quenching electronics. We then test four InGaAs-InP APDs using the ASIC, operating both in the free-running and gated modes, to study more general behavior. We investigate not only the standard parameters under different working conditions but also parameters such as charge persistence and quenching time. We also use the multiple trapping model to account for the afterpulsing behavior in the gated mode, and further propose a model to take account of the afterpulsing effects in the free-running mode. Our results clearly indicate that the performance of APDs with an on-chip quenching circuit significantly surpasses the conventional quenching electronics and makes them suitable for practical applications, e.g., quantum cryptography.