This study presents a global sensitivity analysis to simplify a surrogate-model-based uncertainty quantification of a crude distillation unit with a large number of uncertainties. To overcome the computational limitation of a conventional surrogate model-based approach where the number of simulations required grows exponentially as the input dimension increases, a novel two-stage approach was proposed in this study: in the first stage, a multiplicative dimensional reduction method is applied to identify factors that exert the highest influence on the model outputs. In the second stage, the Gaussian process regression is. exploited for uncertainty quantification from the simplified model derived in the first stage. As a result, the computational efforts for uncertainty quantification were significantly reduced (approximately more than 95%) compared to the conventional Quasi Monte Carlo, while the predicted density functions by the proposed method closely matched with those from the Quasi Monte Carlo. The proposed two-stage approach was executed for sensitivity analysis and uncertainty quantification of a crude distillation unit by an interface between MATLAB and HYSYS. The economic revenue and the operating cost per unit of crude oil processed were selected as the output of interests for the crude distillation unit. The global sensitivity analysis result showed that the flow rates of crude oil and naphtha products are critical for both the economic revenue and the operating cost.