[Purposes] This paper aims to address the issue that the existing terrain complexity error evaluation methods are subjective and lack error analytic formulas. [Methods] The mean square error expressions for local relief, local standard deviation, local rugosity, and local total curvature were derived by using error propagation law. The error estimation model for compound terrain complexity index (CTCI), namely CEEM was constructed by error transfer of compound terrain factors. The effectiveness of CEEM was verified by the simulated digital elevation model (DEM), and the generalization experiment of CEEM was carried out by using the entity DEM of three different landform regions. [Findings] Under the influence of different noises, the maximum values of CEEM’s mean error, mean square error, residual error, and mean absolute percentage error are ?2.1×10?3, 7.99×10?6, 8.4×10?3, and 22.8%, respectively, with an absolute coefficient of above 0.961. The overall error of CEEM is small. There are differences in the extraction error of terrain complexity of different landform types, and the experimental statistical results show that the error size in descending order is high mountain, middle mountain, and hill. [Conclusions] The extraction error of terrain complexity can be quantitatively described by CEEM, which provides a reference for extracting compound terrain complexity index in different complex landform regions.