Due to the limitations of processing errors, test conditions and other factors, geometric similarity errors in scale tests of steel structure joints are difficult to avoid, but the research on this error is little known. Based on the similarity theory and the basic idea of the component method, this paper deduces the similar macro conditions of beam–column end-plate connections and derives the main influencing factors of geometric similarity of these types of structures. Aiming at the factor of the thickness of the end-plate, the formation mechanism of the geometrically incomplete similarity error of this type of node was studied. Through the establishment of accurate finite element models for parameterized analysis, the influence of end plate thickness on incomplete similarity error is analyzed. Based on this model and linear regression analysis methods, the prediction formulas of geometric incomplete similarity errors of beam–column end-plate connections have been established, which can significantly reduce similar errors due to end plate thickness. This article aims to propose a method for simulating the distribution of incompletely similar errors and provide a reference for the research of similar problems.