Linear approximation methods are widely used for constructing distributed power dispatch models to reduce the computational complexity of nonlinear dispatch optimization. Existing studies on linearization mainly focus on the approximation errors in the constraints of distributed power dispatch models. Based on the optimality condition of the distributed power dispatch model, it is pointed out that constraint linearization not only introduces errors into the constraints but also generates a Lagrange-multiplier-related term in the dispatch objective function. Based on this, a linearization method of distributed power dispatch model is proposed. By utilizing the Lagrangian dual information iteratively obtained in typical distributed algorithms for solving distributed power dispatch models, the formulation of the proposed Lagrange-multiplier-related term is derived. The case study shows that, by compensating for this Lagrange-multiplier-related bias term in the objective function of the dispatch model, the solution accuracy and computational efficiency of the linear model for distributed power dispatch optimization are improved by approximately 43.7% and 40.1%, respectively.