The economic dispatch of multi-area power systems can be regarded as a new constrained optimization problem in multi-agent network, which comparing to the problems that have been researched includes the global and local decision variables, as well as about their local equality constraints. For solving this problem, a modified distributed gradient algorithm is proposed by combining two existing methods. Firstly, the interaction prediction and balance method is used to solve the global and local decision variables alternately with a coordination center. Secondly, the optimization problem in coordination center is transformed into an existing constrained optimization problem in multi-agent network and solved by using the distributed primal-dual sub-gradient optimization algorithm. As thus, the multi-area economic dispatch problem can be optimized in a fully distributed way without any coordination center. Through the numerical testing of IEEE-24 bus system divided into three interconnected areas, the three areas can converge to the same global optimal solutions, and compared with the calculation results of centralized optimization, the correctness of the algorithm is verified.