With the fast development of unmanned aerial vehicles (UAVs), reliable UAV communication is becoming increasingly vital. The channel knowledge map (CKM) is a crucial bridge connecting the environment and the propagation channel that may visually depict channel characteristics. This paper presents a comprehensive scheme based on a UAV-assisted channel measurement system for constructing the CKM in real-world scenarios. Firstly, a three-dimensional (3D) CKM construction scheme for real-world scenarios is provided, which involves channel knowledge extraction, mapping, and completion. Secondly, an algorithm of channel knowledge extraction and completion is proposed. The sparse channel knowledge is extracted based on the sliding correlation and constant false alarm rate (CFAR) approaches. The 3D Kriging interpolation is used to complete the sparse channel knowledge. Finally, a UAV-assisted channel measurement system is developed and CKM measurement campaigns are conducted in campus and farmland scenarios. The path loss (PL) and root mean square delay spread (RMS-DS) are measured at different heights to determine CKMs. The measured and analyzed results show that the proposed construction scheme can effectively and accurately construct the CKMs in real-world scenarios.