This paper presents the effect of eccentricity and surface roughness on the probabilistic performance of two axial groove hydrodynamic journal bearing. In general, it is difficult to quantify experimentally the variabilities involved in dynamic responses of the hydrodynamic bearing due to the randomness involved in surface asperity and eccentricity ratio. The deterministic models available for the analysis of the bearings are not capable to include such uncertainties. These uncertainties arise from the manufacturing imperfections, misalignment of the bearing, frictional wear, uncertain operating condition, model inaccuracy. To simulate such variabilities, Monte Carlo simulation (MCS) is carried out. Stochastic steady-state and dynamic coefficients are obtained by solving the Reynolds equation using the surrogate-based finite difference method. Sensitivity analysis of the performance parameters with respect to stochastic input parameters is portrayed. The moving least square (MLS) model is constructed as the surrogate to increase the computational efficiency. The significant influences of stochastic input parameters such as surface roughness and eccentricity ratio are observed on the random hydrodynamic performance of two axial groove journal bearing.