Past decades have seen the great potential of generative machine learning in molecular design while also exposed the gap between research contributions and practical applications. Considering the expensive-to-evaluate nature of molecular properties and hard-to-satisfy validity of molecular structures, this paper tackles molecular design from graph Bayesian optimization viewpoint, i.e., generating feasible and optimal molecular graph with compatible features given limited number of evaluations. Our proposed method, BoGrape, uses shortest-path graph kernels to measure the similarity between molecules and utilizes mixed-integer programming to allow global exploration of molecular space while maintaining the feasibility of generated candidates. Preliminary results show promising performance of BoGrape.