Time series forecasting is widely applied in various fields, such as traffic planning and weather forecasting. However, real-world time series often exhibit intricate temporal variations, which make forecasting challenging. Many existing methods either focus on modeling time series at fixed or limited scales, restricting the diversity of feature scales, or concentrate primarily on long-term dependencies across scales while neglecting intra-scale information interactions. Furthermore, due to the global nature of the self-attention mechanism, Transformers exhibit poor performance in handling local interactions and short-term dependencies. To address these challenges, we propose AMSformer, an adaptive Transformer with convolutional multi-scale feature interactions. First, we integrate spatial pyramid multi-receptive field convolutional features into the Transformer architecture, mitigating the limitations of local information interaction and single-feature representation. Additionally, we propose a bidirectional fusion interaction module that enables multi-scale fusion across hierarchical features between the Transformer and CNN. We also introduce an adaptive router that dynamically selects the optimal time scale for adaptive multi-scale modeling. Extensive experiments on nine real-world datasets demonstrate that our model outperforms state-of-the-art methods in terms of prediction accuracy.