Biomedical Event Causal Relation Extraction (BECRE) is an important task in biomedical information extraction. Existing methods usually use pre-trained language models to learn semantic representations and then predict the event causal relation. However, these methods struggle to capture sufficient cues in biomedical texts for predicting causal relations. In this paper, we propose a Path Reasoning-based Relation-aware Network (PRRN) to explore deeper cues for causal relations using reinforcement learning. Specifically, our model reasons the relation paths between entity arguments of two events, namely entity relation path, which connects the two biomedical events through the multi-hop interactions between entities to provide richer cues for predicting event causal relations. In PRRN, we design a path reasoning module based on reinforcement learning and propose a novel reward function to encourage the model to focus on the length and contextual relevance of entity relation paths. The experimental results on two datasets suggest that PRRN brings considerable improvements over the state-of-the-art models.