IntraOcular Pressure (IOP) is one of the most informative factors for monitoring the eye-health. This is usually measured by tonometers. However, the outputs of the tonometers depend on the physical and geometrical properties of the cornea. Therefore, the common practice is to develop a numerical model to generate some correction factors. The main challenge here is the accuracy and efficiency of a numerical model in predicting the IOP and Dynamic Corneal Response (DCR) of each patient. This study addresses this issue by developing a two-step surrogate model based on adaptive sparse Polynomial Chaos Expansion (PCE) for fast and accurate prediction of the IOP. In this regard, first, an FE model of the cornea has been developed to predict the DCR parameters. This FE model has been replaced with a PCE-based surrogate model to speed up the simulation step. The uncertainties in the geometry and material model of the cornea have been propagated through the surrogate model to estimate the distributions of the DCR parameters. In the second step, the combination of DCR parameters and the input parameters provide a proper parameter space for developing an efficient data-driven PCE model to predict the IOP. Moreover, sensitivity analysis by using PCE-based Sobol indices has been performed. The results demonstrate the accuracy and efficiency of the proposed method in predicting the IOP. Sensitivity analysis revealed that IOP measurement was influenced mostly by deflection amplitude and applanation time. The analysis indicates the importance of the interactions between the parameters.