Multimodal Large Language Models (MLLMs) have been widely adopted as MLLM-as-a-Judges due to their strong alignment with human judgment across various visual tasks. However, most existing judge models are optimized for single-task scenarios and struggle to generalize to diverse contexts, which is a critical requirement for reliable evaluation. To address this limitation, we propose Multi-Task Reinforcement Learning for MLLM-as-a-Judge (MT-RL-Judge), a framework that jointly optimizes the judge model across multiple tasks, leveraging the generalization capabilities of RL. Experimental results against several strong baselines demonstrate that MT-RL-Judge outperforms strong baselines in both judgment consistency and correlation with human preferences. Furthermore, our approach exhibits robust generalization on out-of-distribution tasks, further validating its effectiveness.