It is fundamentally challenging for robots to serve as useful assistants in human environments because this requires addressing a spectrum of sub-problems across robotics, including perception, language understanding, reasoning, and planning. The recent advancements in Multimodal Large Language Models (MLLMs) have demonstrated their exceptional abilities in solving complex mathematical problems, mastering commonsense and abstract reasoning. This has led to the recent utilization of MLLMs as the brain in robotic systems, enabling these models to conduct high-level planning prior to triggering low-level control actions for task execution. However, it remains uncertain whether existing MLLMs are reliable in serving the brain role of robots. In this study, we introduce the first benchmark for evaluating Multimodal LLM for Robotic (MMRo) benchmark, which tests the capability of MLLMs for robot applications. Specifically, we identify four essential capabilities perception, task planning, visual reasoning, and safety measurement that MLLMs must possess to qualify as the robot's central processing unit. We have developed several scenarios for each capability, resulting in a total of 14 metrics for evaluation. We present experimental results for various MLLMs, including both commercial and open-source models, to assess the performance of existing systems. Our findings indicate that no single model excels in all areas, suggesting that current MLLMs are not yet trustworthy enough to serve as the cognitive core for robots. Our data can be found in https://mm-robobench.github.io/.