This paper develops a novel N-1 security-constrained coordinated scheduling model of integrated electricity and natural gas system (IEGS) with consideration of gas dynamics and wind power uncertainty. Direct quantile regression method and Monte Carlo simulation are applied to model the uncertainty associated with wind power forecast in scenarios. Then, the bilinear functions of natural gas constraints are transformed to a set of linear constraints based on McCormick envelopes. To integrate gas dynamics with security analysis in IEGS, a linear dynamic gas flow model considering N-1 contingency of pipeline is established by means of big-M method and the fully implicit finite difference method. Finally, the proposed stochastic coordinated scheduling problem of IEGS is formulated as a mixed-integer linear programming model. Numerical experiments are implemented to verify the superior accuracy of the linear dynamic gas flow model and the effectiveness of the proposed stochastic scheduling model.