The elevator dispatch problem(EDP) is a kind of combinatorial optimization problem with the nonlinear objective function and short solving time request. Therefore, we propose a linearization method of the EDP based on the time-space-state network together with the corresponding linear 0-1 integer programming model. In order to solve the model efficiently, we introduce the space dilation method into the sub-gradient iterative process of the Lagrange multiplier and an augmented multiplier update method based on iteration time to make up for the defect of short solving time. The result of a numerical experiment under 500ms respond time shows that the proposed method has better solution quality than the existing heuristic algorithm, shorter solving time than the branch and bound algorithm provided by Gurobi-9.0.1, and can solve the EDP stably and efficiently.