The after-pulsing effect is a common problem in high-speed and low-noise single-photon detection based on single-photon avalanche diodes (SPADs). This article presents a dual anode InGaAs/InP SPAD (DA-SPAD) with two separate anode output ports that can be utilized for discriminating relatively weak avalanche signals, providing a simple and robust configuration of the SPAD-based single-photon detection system. Weak avalanche signals with amplitudes below the amplitude of the parasitic capacitive response of the SPAD were easily detected by the DA-SPAD and a simple subtraction circuit. The gated Geiger-mode performance of the DA-SPAD was also investigated. At a gating frequency of 1 GHz, the detection efficiency was 20.4% with an after-pulse probability of 3.5% at a temperature of -20 °C.