Many crucial scientific problems involve designing novel molecules with desired properties, which can be formulated as a black-box optimization problem over the discrete chemical space. In practice, multiple conflicting objectives and costly evaluations (e.g., wet-lab experiments) make the diversity of candidates paramount. Computational methods have achieved initial success but still struggle with considering diversity in both objective and search space. To fill this gap, we propose a multi-objective Bayesian optimization (MOBO) algorithm leveraging the hypernetwork-based GFlowNets (HN-GFN) as an acquisition function optimizer, with the purpose of sampling a diverse batch of candidate molecular graphs from an approximate Pareto front. Using a single preference-conditioned hypernetwork, HN-GFN learns to explore various trade-offs between objectives. We further propose a hindsight-like off-policy strategy to share high-performing molecules among different preferences in order to speed up learning for HN-GFN. We empirically illustrate that HN-GFN has adequate capacity to generalize over preferences. Moreover, experiments in various real-world MOBO settings demonstrate that our framework predominantly outperforms existing methods in terms of candidate quality and sample efficiency. The code is available at https://github.com/violet-sto/HN-GFN.