Quantum walks (QWs) provide a powerful tool as a quantum simulator to study and understand topological phases. Using such a quantum simulator, some topological phenomena have been discussed. However, all the experimental observations on the topological phenomena in QWs have been restricted to evolution in one dimension (1D) so far. The existing 2D experimental platforms cannot be applied to study topological phenomena due to lack of full control in the position space. Thus, some interesting topological phenomena in the 2D QW that do not exist in the 1D case, e.g., the edge-state-enhanced transport, have not been demonstrated experimentally. Here we report the experimental realization of 2D QW using spatial positions and orbital angular momentum of light. Based on our constructed experimental platform, we have observed 2D topological bound states with vanishing Chern numbers and confirmed the robustness of these bound states with respect to perturbations and disorder, which go beyond what has been known in static systems and are unique to periodically driven systems. Our studies not only represent an important advance in the study of topological phases, but also open up an avenue to explore topological properties in multidimensional QWs.