In many practical application problems, the existence of uncertainty has an impact on the performance of the optimal solution to an optimization problem. When solving optimization problems in uncertain environments, it is often necessary to consider the robustness of the solution. The definition of robustness of an optimal solution usually considers the performance of all solutions in its local neighborhood. In the context of multiobjective optimization, it is a very challenging task to approximate the robust Pareto fronts. Existing robust multi-objective evolutionary algorithms (MOEA) can handle low-dimensional robust multi-objective optimization problems (MOPs), i.e., the dimensionality of the decision variables is less than 10, but often perform poorly for high-dimensional robust MOPs. In this paper, we propose an MOEA, called MOEA/D-AECC (Decomposition-based Multiobjective Evolutionary \mbox{Algorithm} Assisted by Autoencoder and Cooperative Coevolution, MOEA/D-AECC), which combines \mbox{autoencoder} as well as co-evolutionary methods, for solving high-dimensional robust MOPs with low eff-ective dimension. The algorithm utilizes two different populations to optimize the original MOPs and the corresponding robust MOPs, respectively. To improve the ability to handle high-dimensional problems, the algorithm utilizes an autoencoder for dimensionality reduction in order to extract the low-dimensional features of the high-dimensional data. The descent directions are learned by reconstructing these low-dimensional features, then new \mbox{solutions} are generated by sampling along these descent directions. Finally, the performance of MOEA/D-AECC is tested on a set of high-dimensional robust MOPs with low effective dimensions in this paper. The experimental results show that the performance of MOEA/D-AECC is significantly better than several other representative robust MOEA.