In stochastic simulations, input model uncertainty may significantly impact output estimation accuracy. Although variance reduction techniques alleviate the computational burden, input model uncertainty remains unaddressed. Among several variance reduction techniques, we propose a robust version of the importance sampling method. We formulate a min-max optimization problem for finding a robust sampling density for simulation inputs considering a parametric uncertainty set that represents candidates of the true input distribution. We utilize the Bayesian optimization framework for solving the outer problem and the barrier method for tackling the inner problem. By incorporating input model uncertainty in the sampling stage, our method effectively allocates simulation effort to improve estimation robustness. Numerical experiments demonstrate the advantages of the proposed method over a benchmark model assuming a precisely known input model. Our approach produces more accurate output estimation (i.e., an estimator with lower variance), highlighting its robustness and potential applicability in a variety of situations.