To achieve fast and high⁃accuracy detection with single⁃photon light detection and ranging（LiDAR), this paper designs a high⁃flux and high⁃repetition⁃rate single⁃photon LiDAR system and proposes a waveform correction method tailored for this system. By increasing the photon counting rate, the system significantly reduces the single⁃pixel acquisition time. Meanwhile, the waveform correction method effectively addresses the issues of waveform distortion caused by the dead time of single⁃photon detectors under high⁃flux and high⁃repetition⁃rate conditions, thereby enhancing the inversion accuracy of target signal strength and depth. The system employs a free⁃running single⁃photon detector in the near⁃infrared band with a dead time of 1 200 ns and a laser repetition rate of 3 MHz, and the single⁃pixel acquisition time is set to 1 ms. Simulation and experimental results demonstrate that the proposed method achieves a distance inversion accuracy of 4.9 mm and a photon flux inversion accuracy of 0.16 photons. In the 3D imaging experiment, using a 50 × 50 point⁃to⁃point scanning pattern, the imaging plane fitting accuracy reaches 8 mm, enabling high⁃precision 3D imaging of small UAVs at close range. This study provides a new technical approach for the application of single⁃photon LiDAR in fast imaging fields such as target detection and resource mapping.