Many optimization problems involve performing expensive simulations to evaluate the quality of the input values in terms of multiple objectives and the feasibility of the input values in terms of various constraints. Our goal is to approximate the optimal Pareto set over the small fraction of feasible input values by minimizing the number of simulations. The key scalability challenges include huge design space, the large number of objectives and constraints, and the small fraction of feasible inputs, which can be identified only after performing expensive simulations. Additionally, in various cases, the practitioner prefers specific objectives over others. We propose a novel and efficient preference-aware constrained multi-objective Bayesian optimization approach referred to as PAC-MOO to address these challenges. The key idea is to learn surrogate models for both output objectives and constraints and select the candidate circuit for simulation in each iteration that maximizes the information gained about the optimal constrained Pareto front while factoring in the objective preferences. Our experiments on two real-world analog circuit design optimization problems demonstrate the efficacy of PAC-MOO over prior methods.