We present a compact and lightweight 1.5 μm lidar using a free-running single-photon detector (SPD) based on a multi-mode fiber (MMF) coupling InGaAs/InP negative feedback avalanche diode. The ultimate light detection sensitivity of SPD highly reduces the power requirement of the laser, whilst the enhanced collection efficiency due to MMF coupling significantly reduces the volume and weight of telescopes. We develop a specific algorithm for the corrections of errors caused by the SPD and erbium-doped fiber amplifier to extract accurate backscattering signals. We also perform a comparison between single-mode fiber (SMF) coupling and MMF coupling in the lidar receiver, and the results show that the collection efficiency with MMF coupling is five times higher than that with SMF coupling. In order to validate the functionality, we use the lidar system for the application of cloud detection. The lidar system exhibits the ability to detect both the cloud base height and the thickness of multi-layer clouds to an altitude of 12 km with a temporal resolution of 1 s and a spatial resolution of 15 m. Due to the advantages of compactness and lightweight, our lidar system can be installed on unmanned aerial vehicles for wide applications in practice.