Multimodal Reward Models are critical for aligning Multimodal Large Language Models with human preferences. However, existing reward models offer limited interpretability and struggle to deliver reliable preference judgments in audio-centric scenarios. To address this gap, we propose Audio-Reward-R1, a reasoning-based reward model that supports both audio understanding and audio generation preference tasks. Audio-Reward-R1 formulates reward modeling as a structured reasoning process, producing dimension-level analyses prior to the final preference judgment. To enable reliable reasoning supervision, we construct a high-quality reasoning-enhanced audio preference dataset with structured reasoning traces aligned with preference annotations. Audio-Reward-R1 is first trained via supervised fine-tuning as a cold-start on this reasoning-enhanced dataset, followed by reinforcement learning with verifiable rewards. Finally, we introduce Audio-Reward-Bench, a human-verified evaluation benchmark for evaluating audio reward models across both audio understanding and audio generation preference tasks. Extensive experimental results demonstrate the effectiveness and reliability of Audio-Reward-R1.