To improve the level of emergency management, this paper considers the uncertainty of the travel cost under the influence of an unexpected event to study urban traffic evacuation problem. Firstly, a spatio-temporal coupled network diagram based on the spatio-temporal characteristics of traffic evacuation problem is created, and a quantification method for the travel cost of urban traffic road networks is proposed, which contains a combination of the travel time cost and conflict risk cost. Furthermore, considering the influence of an upper limit to link resource weights for side constraints, a robust optimization model of the priori evacuation strategy based on the budgeted uncertainty set is constructed to minimize the total travel cost of road network evacuation process. Then, the model reconstruction technique is applied to transform the constructed robust model into a mixed integer linear programming model, and an adapted Lagrangian relaxation method is designed to decouple and solve. Finally, the SiouxFalls network is used for arithmetic analysis and the numerical results show that the growth rates of travel time cost and conflict risk cost increase by about 29.13% and 236.46%, respectively, with the growth of uncertainty set and model size. The model budget parameter is controlled in a certain interval, which can better trade off the robustness and optimality of solutions. The applicability of the proposed method in larger scale network calculations is verified through a case study of the Nanjing regional road network, and the results show the proposed method can obtain high-quality feasible solutions within fewer number of iterations than the traditional Lagrangian relaxation method. The results of this study can provide ideas for emergency command authorities to develop reliable traffic evacuation strategies.