Multimodal Large Language Models (MLLMs) have shown promising results in various tasks, but their ability to perceive the visual world with deep, hierarchical understanding similar to humans remains uncertain. To address this gap, we introduce CONSTRUCTURE, a novel concept-level benchmark to assess MLLMs’ hierarchical concept understanding and reasoning abilities. Our goal is to evaluate MLLMs across four key aspects: 1) Understanding atomic concepts at different levels of abstraction; 2) Performing upward abstraction reasoning across concepts; 3) Achieving downward concretization reasoning across concepts; and 4) Conducting multi-hop reasoning between sibling or common ancestor concepts. Our findings indicate that even state-of-the-art multimodal models struggle with concept structure reasoning (e.g., GPT-4o averages a score of 62.1%). We summarize key findings of MLLMs in concept structure reasoning evaluation. Morever, we provide key insights from experiments using CoT prompting and fine-tuning to enhance their abilities.