We present a fully integrated InGaAs/InP negative feedback avalanche diode (NFAD) based free-running single-photon detector (SPD) designed for accurate lidar applications. A free-piston Stirling cooler is used to cool down the NFAD with a large temperature range, and an active hold-off circuit implemented in a field programmable gate array is applied to further suppress the afterpulsing contribution. The key parameters of the free-running SPD including photon detection efficiency (PDE), dark count rate (DCR), afterpulse probability, and maximum count rate (MCR) are dedicatedly optimized for lidar application in practice. We then perform a field experiment using a Mie lidar system with 20 kHz pulse repetition frequency to compare the performance between the free-running InGaAs/InP SPD and a commercial superconducting nanowire single-photon detector (SNSPD). Our detector exhibits good performance with 1.6 Mcps MCR (0.6 μs hold-off time), 10% PDE, 950 cps DCR, and 18% afterpulse probability over 50 μs period. Such performance is worse than the SNSPD with 60% PDE and 300 cps DCR. However, after performing a specific algorithm that we have developed for afterpulse and count rate corrections, the lidar system performance in terms of range-corrected signal (Pr2) distribution using our SPD agrees very well with the result using the SNSPD, with only a relative error of ∼2%. Due to the advantages of low-cost and small size of InGaAs/InP NFADs, such detector provides a practical solution for accurate lidar applications.