This article presents a model predictive control (MPC) based multitime scale co-optimized dispatch for integrated electricity and natural gas system (IEGS) considering the bidirectional interactions and renewable uncertainties. In the proposed model, optimal dispatch is extended into three substages optimization problems of day-ahead, intraday, and real-time to coordinate the economy and accuracy of operations. The different optimization strategy is designed in each dispatching stage according to the operating characteristics of multienergy coupled units and high-penetration intermittent wind power. In the day-ahead stage, the unit commitment is tackled to arrange the start-stop plan of slow-response units, maintained in intraday and real-time stages to ensure full-term optimal economic operation. In the intraday stage, MPC-based rolling optimization is implemented to obtain the unit output scheme with the lowest operating cost target. Furthermore, the output scheme is rolling adjusted in the real-time stage based on the ultrashort-term forecast value, and a closed-loop feedback mechanism is introduced to achieve accurate power balance. In each stage, stochastic decision-making is executed based on the stochastic scenario method, efficiently capturing the uncertainty in IEGS. Besides, the proposed nonlinear model is transformed into a mixed-integer second-order cone programming problem using McCormick relaxation, which can be efficiently solved by commercial solvers. Simulation results on IEEE39-Gas20 and IEEE118-GAS40 test systems demonstrate the superiority of the proposed method in operational economy and wind power utilization, and also verify the effectiveness of the method to accurately track random fluctuations without obvious computational burden.