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.　©　2019　IEEE.