Long-term time series forecasting is an important and challenging task. Due to the mixture of various variations in the time series, its patterns are complex, making it difficult to model long-term dependencies. To this end, we propose a multi-granularity dependency modeling and interaction network (MDMIN) to achieve more effective long-term forecasting. Unlike most existing methods, MDMIN models long-term dependencies in a more detailed manner. Its multi-granularity convolution module could simultaneously capture temporal variations of relative long-term, medium-term, and short-term granularities, modeling multi-granularity dependencies. In addition, the weight optimization mechanism in MDMIN could adaptively learn the importance of features and optimize weights according to the importance, enhancing important and suppressing redundant feature representations. To refine the modeling of long-term dependencies through multi-granularity information, MDMIN applies the self-attention mechanism of Transformer to interact the cross-granularity dependencies, and then make predictions. Comprehensive experiments on 8 popular and widely used benchmarks show that MDMIN achieves more effective long-term forecasting and has strong competitiveness.