Variational Graph Autoencoders (VAGE) emerged as powerful graph representation learning methods with promising performance on graph analysis tasks. However, existing methods typically rely on Graph Convolutional Networks (GCN) to encode the attributes and topology of the original graph. This strategy makes it difficult to fully learn high-order neighborhood information, which weakens the capacity to learn higher-quality representations. To address the above issues, we propose the Multi-order Variational Graph Autoencoders (MoVGAE) with co-learning of first-order and high-order neighborhoods. GCN and Multi-order Graph Convolutional Networks (MoGCN) are utilized to generate the mean and variance for the variational autoencoders. Then, MoVGAE uses the mean and variance to calculate node representations. Specifically, this approach comprehensively encodes first-order and high-order information in the graph data. Finally, the decoder reconstructs the adjacency matrix by performing the inner product of the representations. Experiments with the proposed method were conducted on node classification, node clustering, and link prediction tasks on real-world graph datasets. The results demonstrate that MoVGAE achieves state-of-the-art performance compared to other baselines in various tasks. Furthermore, the robustness analysis verifies that MoVGAE has obvious advantages in the processes of graph data with insufficient attributes and topology.