Multivariate time-series (MTS) forecasting is a challenging task in many real-world non-stationary dynamic scenarios. In addition to intra-series temporal signals, the inter-series dependency also plays a crucial role in shaping future trends. How to enable the model’s awareness of dependency information has raised substantial research attention. Previous approaches have either presupposed dependency constraints based on domain knowledge or imposed them using real-time feature similarity. However, MTS data often exhibit both enduring long-term stable relationships and transient short-term interactions, which mutually influence their evolving states. It is necessary to recognize and incorporate the complementary dependencies for more accurate MTS forecasting. The frequency information in time series reflects the evolutionary rules behind complex temporal dynamics, and different frequency components can be used to well construct interactive dependency structures with varying states between variables. To this end, we propose FCDNet, a concise yet effective complementary dependency modeling framework for multivariate time-series forecasting. Specifically, FCDNet overcomes the above limitations by applying two lightweight dependency constructors to help extract stable static and dynamic varying dependency information adaptively from long short-term multi-level frequency patterns. With the growth of input variables, the number of trainable parameters in FCDNet only increases linearly, which is conducive to the model’s scalability and avoids over-fitting. Additionally, adopting a frequency-based perspective can effectively mitigate the influence of noise within MTS data, which helps capture more genuine dependencies. The experimental results on six real-world datasets from multiple fields show that FCDNet significantly exceeds strong baselines, with an average improvement of 6.82% on MAE, 4.98% on RMSE, and 4.91% on MAPE. In addition, the ability of FCDNet to jointly learn high-quality static and dynamic graph structures is demonstrated empirically. Our source codes are publicly available at https://github.com/onceCWJ/FCDNet.