Accurate network traffic prediction is critical for enhancing network security and optimizing resource allocation. Existing prediction methods struggle to capture feature correlations across different scales and periods within traffic time series, leading to poor performance in handling complex periodic patterns and irregular traffic fluctuations. To address this issue, we propose a novel Multi-Scale and Multi-Period Transformer model (Mmformer), which includes a Multi-Scale Block, Multi-Period Time Blocks and a Multi-Feature Encoder. Firstly, the Multi-Scale Block utilizes a parallel architecture to extract multiple 1D temporal features across different time scales. Additionally, Multi-Period Time Blocks use Fast Fourier Transform to convert 1D temporal features into multiple 2D periodic feature matrices. These blocks then employ 2D convolutional networks to efficiently extract local periodic features. Finally, the model introduces the Multi-Feature Encoder based on an improved Transformer to learn the complex relationships between multi-scale and multi-period features, effectively capturing the long-distance dependencies and correlations within temporal features. Experimental results indicate that Mmformer reduces MAPE by 23.17% compared to leading methods, highlighting its superior accuracy and generalization.