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This paper presents an uncontrolled intersection-passing algorithm with an integrated approach of stochastic model-predictive control and prediction uncertainty estimation for autonomous vehicles. The proposed algorithm is designed to utilize information from sensors mounted on the autonomous vehicle and high-definition intersection maps. The proposed algorithm is composed of two modules, namely target state prediction and a motion planner. The target state prediction module has predicted the future behavior of intersection-approaching vehicles based on human driving data. The recursive covariance estimator has been utilized to estimate the prediction uncertainty for each approaching vehicle. The desired driving mode has been determined based on the uncontrolled intersection theory. The estimated prediction uncertainty has been used to define the probability distribution of the stochastic model-predictive controller to cope with time-varying uncertainty characteristics of the perception algorithm. The constrained stochastic model-predictive controller based on safety indexes has determined the desired longitudinal acceleration. The proposed robust intersection-passing algorithm has been evaluated via computer simulation based on Monte Carlo simulation with a sensor model. The simulation results showed that the proposed algorithm guarantees the minimum safety constraints and improves the ride comfort at uncontrolled intersections by estimating the uncertainty of sensors and prediction.