In the past decades, a number of surrogate-assisted evolutionary algorithms (SAEAs) have been developed to solve expensive multiobjective optimization problems (EMOPs). However, most existing SAEAs focus on low-dimensional optimization problems, since a large number of training samples are required (which is unrealistic for EMOPs) to build an accurate surrogate model for high-dimensional problems. In this paper, an SAEA with Dimension Dropout is proposed to solve high-dimensional EMOPs. At each iteration of the proposed algorithm, it randomly selects a part of the decision variables by Dimension Dropout, and then optimizes the selected decision variables with the assistance of surrogate models. To balance the convergence and diversity, those candidate solutions with good diversity are modified by replacing the selected decision variables with those optimized ones (i.e., decision variables from some better-converged candidate solutions). Eventually, the new candidate solutions are evaluated using expensive functions to update the archive. Empirical studies on ten benchmark problems with up to 200 decision variables demonstrate the competitiveness of the proposed algorithm.