Due to the volatile and correlated nature of wind speed, a high share of wind power penetration poses challenges to power system production simulation. Existing power system probabilistic production simulation approaches are in short of considering the time-varying characteristics of wind power and load, as well as the correlation between wind speeds at the same time, which brings about some problems in planning and analysis for the power system with high wind power penetration. Based on universal generating function (UGF), this paper proposes a novel probabilistic production simulation approach considering wind speed correlation. UGF is utilized to develop the chronological models of wind power that characterizes wind speed correlation simultaneously, as well as the chronological models of conventional generation sources and load. The supply and demand are matched chronologically to not only obtain generation schedules, but also reliability indices both at each simulation interval and the whole period. The proposed approach has been tested on the improved IEEE-RTS 79 test system and is compared with the Monte Carlo approach and the sequence operation theory approach. The results verified the proposed approach with the merits of computation simplicity and accuracy.