The AC optimal power flow (AC-OPF) problem is a challenging and crucial task in power system operation, aiming to optimize generation cost while satisfying operational constraints. To enhance the training and computational efficiency of solving AC-OPF problems in large-scale systems, we propose DeepOPF-D, a novel decentralized community-based machine learning approach, to learn the load-solution mapping in a decentralized manner. First, based on the complex network theory and electrical properties, the Louvain algorithm is leveraged for community detection in power grids, which identifies multiple non-overlapping communities. Then, a feature and prediction variable decomposition method is proposed to partition the loads and bus voltages of the entire system into smaller groups according to the identified communities. Subsequently, for each community, a deep neural network (DNN) model is trained to learn the mapping between the loads and the voltages of non-zero injection buses within that community. After obtaining the predictions of all DNN models, the zero-injection bus voltages are recovered using the Kron reduction method. Through numerical tests on the IEEE 30-bus system, we validate the effectiveness of DeepOPF-D in terms of training efficiency and feasibility, by comparing it with the state-of-the-art centralized machine learning approach.