High detection efficiency appears to be associated with a high afterpulse probability for InP-based single-photon avalanche diodes. In this paper, we present a new hybrid quenching technique that combines the advantages of both fast active quenching and high-frequency gated-passive quenching, with the aim of suppressing higher-order afterpulsing effects. Our results showed that the hybrid quenching method contributed to a 10% to 85% reduction of afterpulses with a gate-free detection efficiency of 4% to 10% at 1.06 $\mathsf{\mu }$m, with 40 ns dead time, compared with the counter-based hold-off method. With the improvement of the afterpulsing performance of high-frequency gated single-photon detectors, especially at relatively high average detection efficiencies with wide gate widths, the proposed method enables their use as high-performance free-running detectors.