Detecting the community structures of multi-layer networks is important for exploring the node functions and revealing the potential network structures. However, the existing methods mainly rely on the intra-layer features and manual labels, which leads to the high computational overhead and cannot ensure the robustness and accuracy in networks with complex community structures. To solve the above problems, this paper proposes a network feature-augmentation contrastive constraint method (named as NFACC), which achieves the high accuracy and robustness by contrasting the feature-augmented and original multi-layer networks. Specifically, NFACC consists of two main models, i.e., a feature-augmented network generation model and a contrastive learning-based node representation model. Firstly, NFACC integrates the intra-layer and inter-layer features of multi-layer networks to form an optimizable feature-augmented network based on the generation model. Then, it obtains the low-dimensional representations of both the augmented network and each layer of the multi-layer network based on the node representation model. By training these two models, NFACC further merges the intra-layer and inter-layer features and improves the robustness against complex network structures. Finally, NFACC achieves accurate community detection through the trained node representations. Extensive experiments demonstrate that the proposed NFACC method outperforms the state-of-the-art methods in detecting the community structure of multi-layer networks.