In light of recent progress in video editing, deep learning models focusing on both spatial and temporal dependencies have emerged as the primary method. However, these models suffer from the quadratic computational complexity of traditional attention mechanisms, making them difficult to adapt to long-duration and high-resolution videos. This limitation restricts their applicability in practical contexts such as real-time video processing. To tackle this challenge, we introduce a method to reduce both time and space complexity of these systems by proposing VRWKV-Editor, a novel video editing model that integrates a linear spatio-temporal aggregation module into video-based diffusion models. VRWKV-Editor leverages bidirectional weighted key-value recurrence mechanism of the RWKV transformer to capture global dependencies while preserving temporal coherence, achieving linear complexity without sacrificing quality. Extensive experiments demonstrate that the proposed method achieves up to 3.7x speedup and 60% lower memory usage compared to state-of-the-art diffusion-based video editing methods, while maintaining competitive performance in frame consistency and text alignment. Furthermore, a comparative analysis we conducted on videos with different sequence lengths confirms that the gap in editing speed between our approach and architectures with self-attention becomes more significant with long videos.