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The increased distributed generators (DGs) have exacerbated voltage violations in active distribution networks (ADNs). Local reactive power control of DG inverters can realize a fast response to frequent voltage fluctuations. However, commonly used model-based voltage control depends upon accurate network parameters and entire ADN data, which may cause the sensitive information leakage of ADN and DG behaviors in practical operation. In this article, a cloud-edge collaboration-based local voltage control strategy for DGs is proposed with privacy preservation. First, a local voltage control framework is established based on cloud-edge collaboration, in which a surrogate model is built based on the graph convolutional neural networks to estimate the ADN voltages. By transferring the surrogate model, the edge side can obtain the exact voltage estimation in the local curve tuning process without the authority of the whole ADN data, preserving the network parameters of ADN. Then, the interarea coordination based on federated learning is proposed to realize the parameter updating of DG control curves, which can achieve better voltage control performance. By updating surrogate submodels based on private data distributed across multiple edge devices, federated learning can effectively preserve DG behaviors. Finally, the effectiveness and adaptability of the proposed control strategy are validated using the modified IEEE 33-node system. The proposed local DG control strategy can effectively cope with voltage problems and enhance the adaptability to variations in practical operation states while considering privacy preservation.