Graph Retrieval-Augmented Generation (GraphRAG) has shown great effectiveness in enhancing the reasoning abilities of Large Language Models (LLMs) by leveraging graph structures for knowledge representation and modeling complex real-world relationships. However, existing GraphRAG methods still face significant bottlenecks when handling complex problems that require multi-hop reasoning, as their query and retrieval phases are largely based on pre-defined heuristics and do not fully utilize the reasoning potentials of LLMs. To address this problem, we propose GraphRAG-R1, an adaptive GraphRAG framework by training LLMs with process-constrained outcome-based reinforcement learning (RL) to enhance the multi-hop reasoning ability. Our method can decompose complex problems, autonomously invoke retrieval tools to acquire necessary information, and perform effective reasoning. Specifically, we utilize a modified version of Group Relative Policy Optimization (GRPO) that supports rollout-with-thinking capability to train the model. Next, we design two process-constrained reward functions. To handle the shallow retrieval problem, we design a Progressive Retrieval Attenuation (PRA) reward to encourage essential retrievals. Then, to handle the over-thinking problem, we design a Cost-Aware F1 (CAF) reward to balance the model performance with computational costs. We further design a phase-dependent training strategy, containing three training stages corresponding to cold start and these two rewards. These stages empower GraphRAG with format following, behavior shaping, and smartness optimization abilities, respectively. Lastly, our method adopts a hybrid graph-textual retrieval to improve the reasoning capacity. Extensive experimental results demonstrate that GraphRAG-R1 significantly boosts LLM capabilities in solving complex reasoning problems compared to state-of-the-art GraphRAG methods on both in-domain and out-of-domain datasets. Furthermore, our framework can be flexibly integrated with various existing retrieval methods, consistently delivering performance improvements.