Real-time applications require voice conversion models with streaming conversion capabilities, and streaming voice conversion faces significant challenges due to limited future information. To address this challenge, we propose DualVC, a dual-mode neural voice conversion approach that supports both streaming and non-streaming modes using jointly trained separate network parameters. Furthermore, we propose intra-model knowledge distillation and hybrid predictive coding (HPC) to enhance the performance of streaming conversion.Additionally, we incorporate data augmentation to train a noise-robust autoregressive decoder, improving the model's performance on long-form speech conversion. Experimental results demonstrate that the proposed model outperforms the baseline models in the context of streaming voice conversion, while maintaining comparable performance to the non-streaming topline system that leverages the complete context, albeit with a latency of only 252ms.