In recent years, Graph Neural Network (GNN) approaches with enhanced knowledge graphs (KG) perform well in question answering (QA) tasks. One critical challenge is how to effectively utilize interactions between the QA context and KG. However, existing work only adopts the identical QA context representation to interact with multiple layers of KG, which results in a restricted interaction. In this paper, we propose DRLK (Dynamic Hierarchical Reasoning with Language Model and Knowledge Graphs), a novel model that utilizes dynamic hierarchical interactions between the QA context and KG for reasoning. DRLK extracts dynamic hierarchical features in the QA context, and performs inter-layer and intra-layer interactions on each iteration, allowing the KG representation to be grounded with the hierarchical features of the QA context. We conduct extensive experiments on four benchmark datasets in medical QA and commonsense reasoning. The experimental results demonstrate that DRLK achieves state-of-the-art performances on two benchmark datasets and performs competitively on the others.