Wear is the main failure form of the gear transmission interface, runs through the whole life cycle of gear service, and the distributed error of the tooth surface due to the introduced assembly error will make the actual meshing state of the tooth surface different from the ideal meshing state, thus affecting the tooth surface wear trajectory and state. Therefore, considering the coupling relationship between assembly error and tooth surface contact analysis, the variation laws of the wear amount of the gear transmission interface of the variable hyperbolic circular-arc-tooth-trace cylindrical gear were studied under the consideration of assembly error in this article. Based on the tooth surface contact analysis method and Hertz contact theory, the transient linear load, the combined radius of curvature, the length axis and short axis of the contact ellipse, and the instantaneous sliding velocity were calculated. Through revising the calculation method of adhesive wear of variable hyperbolic circular-arc-tooth-trace cylindrical gears, the correlations between the tooth surface wear amount and gear parameters of variable hyperbolic circular-arc-tooth-trace cylindrical gears under different assembly errors were analyzed. The results show that the maximum wear occurs at the root of the tooth, and the wear at the indexing circle approaches zero, whether it is standard installation or non-standard installation. The vertical axial error and horizontal axial error have little effect on the wear, while the center distance error will aggravate the wear. The proposed method comprehensively considers the influence of assembly error and gear parameters on tooth surface wear, and this method can provide a theoretical reference for the design and analysis of anti-wear, wear reduction, and life extension of variable hyperbolic circular-arc-tooth-trace cylindrical gear tooth surface.