Abstract: The evaluation and security defense of the extreme events in a power system is an important topic to improve the resilience of the power system, in which the simulation for the black-start restoration of the power system with high renewable energy penetration after the blackout is of great significance. Under this background, an optimization model for the transmission system black-start restoration considering the uncertainty of wind power output is proposed in this paper. First of all, the uncertainty of wind power outputs and the initial SOC of the energy storage equipment is described by the multi-scenarios stochastic optimization. The coordinated optimization of the units, the branch lines, and the load restoration in the black-start restoration is established. Setting the maximum of the sum of restored load powers and the sum of wind power output powers during the restoration as the main optimization objective, a power system black-start restoration model is built to satisfy the multi-scenarios. Second, the power flow equations in the model are linearized, and a new linearized modeling for the thermal power units is proposed to solve the non-convex & nonlinear challenges and to form a mixed integer linear programming model. Then, in view of the inefficiency caused by the scenario increase, the L-shaped algorithm is utilized to solve the model. Finally, the New England 10-generator 39-bus power system is employed to verify the feasibility and validity of the proposed model and algorithm.