The task of reasoning over Knowledge Graphs (KGs) poses a significant challenge for Large Language Models (LLMs) due to the complex structure and large amounts of irrelevant information. Existing LLM reasoning methods overlook the importance of compositional learning on KG to supply with precise knowledge. Besides, the fine-tuning and frequent interaction with LLMs incur substantial time and resource costs. This paper focuses on the Question Answering over Knowledge Graph (KGQA) task and proposes an Explore-then-Determine (EtD) framework that synergizes LLMs with graph neural networks (GNNs) for reasoning over KGs. The Explore stage employs a lightweight GNN to explore promising candidates and relevant fine-grained knowledge to the questions, while the Determine stage utilizes the explored information to construct a knowledge-enhanced multiple-choice prompt, guiding a frozen LLM to determine the final answer. Extensive experiments on three benchmark KGQA datasets demonstrate that EtD achieves state-of-the-art performance and generates faithful reasoning results.