In this study, we explore the potential of using quantum natural language processing (QNLP) to inverse design metal-organic frameworks (MOFs) with targeted properties. Specifically, by analyzing 150 hypothetical MOF structures consisting of 10 metal nodes and 15 organic ligands, we categorize these structures into four distinct classes for pore volume and $H_{2}$ uptake values. We then compare various QNLP models (i.e. the bag-of-words, DisCoCat (Distributional Compositional Categorical), and sequence-based models) to identify the most effective approach to process the MOF dataset. Using a classical simulator provided by the IBM Qiskit, the bag-of-words model is identified to be the optimum model, achieving validation accuracies of 85.7% and 86.7% for binary classification tasks on pore volume and $H_{2}$ uptake, respectively. Further, we developed multi-class classification models tailored to the probabilistic nature of quantum circuits, with average test accuracies of 88.4% and 80.7% across different classes for pore volume and $H_{2}$ uptake datasets. Finally, the performance of generating MOF with target properties showed accuracies of 93.5% for pore volume and 89% for $H_{2}$ uptake, respectively. Although our investigation covers only a fraction of the vast MOF search space, it marks a promising first step towards using quantum computing for materials design, offering a new perspective through which to explore the complex landscape of MOFs.

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