Hyperspectral remote sensing widely uses unmanned aerial vehicles (UAV) as flight platforms for data collection, which has the advantages of flexibility and efficiency. However, due to UAV performance and environmental conditions, it is difficult for sensors to maintain a fixed shooting posture during the collection process, resulting in data misalignment, distortion, and deformation. While UAV positioning systems and inertial measurement devices provide real-time position and posture for hyperspectral cameras, achieving high accuracy often necessitates numerous ground control points for auxiliary geometric correction, which is time-consuming and labor-intensive. Therefore, it is necessary to study an efficient and time-saving data processing method to correct distortions in hyperspectral data acquisition. In order to efficiently and time-saving eliminate distortions in hyperspectral data during the acquisition process, an unmanned aerial vehicle (UAV) push scan hyperspectral camera data acquisition system was designed based on the principle of collinearity equations. The system integrates a high-precision inertial measurement system and synchronously collects LiDAR point cloud data in the measurement area. The high-precision terrain information contained in the LiDAR point cloud was used for geometric correction of hyperspectral data, and the influence of different density point cloud data on the geometric correction results was studied. Experiments have shown that using LiDAR point clouds improves accuracy by 67% compared to using average elevation geometric correction results. The use of LiDAR and hyperspectral cameras for synchronous acquisition has a significant effect on improving the accuracy of hyperspectral data.