Multivariate time series forecasting (MTSF) is a fundamental task in the time series research domain, with numerous practical applications across various fields. However, effectively capturing the dynamic inter-series dependencies remains a significant challenge in MTSF. To address this issue, we propose CRGNet, a novel framework designed to model continuous and significant inter-series causal relationships through an adaptive causal learning block. The framework initiates by generating adaptive node embeddings to capture the temporal variation characteristics of each time series. Subsequently, the adaptive causal learning block dynamically models the evolving inter-series relationships. For the effective identification of inter-series causal relationships, we introduce a Causal-GNN layer that partitions node features into multiple groups using learnable scalers. This layer enhances node representations through convolutional operations, enabling a richer representation of temporal dependencies. In addition, a graph learning method is employed to compute relationship scores based on edge features. A Jacobian regularization function is leveraged to distinguish between causal and confounding relationships, ensuring the model captures true causal links. Finally, the learned features are fused and passed through a projection layer to generate accurate forecasts. Experiments on 10 real-world datasets show that CRGNet surpasses existing baselines, highlighting the vital role of inter-series causal relationships in capturing complex patterns for MTSF.