Video SAR can identify changes in the region of interest and the path of targets through continuous observation of the region of interest and targets irrespective of the weather and day or night. Recently, as the complexity of the region of interest, such as urban areas, has increased, research is being conducted to use drones as payloads for video SAR. The satellite, an existing platform, uses information through multiple antennas, and the distance between the target and the platform is sufficiently far to approximate the speed of the target to detect the moving target. However, the drones cannot approximate the target speed owing to the close distance to the target, and there is a limitation in the payload weight; hence, it is difficult to use multiple antennas. Therefore, this study investigates the process of detecting a moving target using a compressive sensing technique on a short-range platform equipped with a single antenna. Finally, through simulation and real data, it was verified that the video SAR image processing of a moving target based on compression sensing was possible.