Complex distribution shifts are the main obstacle to achieving accurate long-term time series forecasting. Several efforts have been conducted to capture the distribution characteristics and propose adaptive normalization techniques to alleviate the influence of distribution shifts. However, these methods neglect the intricate distribution dynamics observed from various scales and the evolving functions of distribution dynamics and normalized mapping relationships. To this end, we propose a novel model-agnostic Evolving Multi-Scale Normalization (EvoMSN) framework to tackle the distribution shift problem. Flexible normalization and denormalization are proposed based on the multi-scale statistics prediction module and adaptive ensembling. An evolving optimization strategy is designed to update the forecasting model and statistics prediction module collaboratively to track the shifting distributions. We evaluate the effectiveness of EvoMSN in improving the performance of five mainstream forecasting methods on benchmark datasets and also show its superiority compared to existing advanced normalization and online learning approaches. The code is publicly available at https://github.com/qindalin/EvoMSN.