This　paper　develops　a　composite　output　consensus　control　protocol　for　a　general　linear　multi-agent　system　subject　to　mismatched　disturbances,　which　incorporates　active　disturbance-rejection　control　and　fully　distributed　adaptive　consensus　control.　To　estimate　and　then　cancel　out　the　effect　of　mismatched　disturbances　on　the　outputs　of　the　agents,　heterogeneous　generalized　equivalent-input-disturbance　estimators　are　constructed　in　the　inner　loop.　Then　a　fully　distributed　adaptive　feedback　controller　is　designed　to　achieve　consensus　control　based　on　the　states　of　the　designed　heterogeneous　observers　for　the　agents.　The　restriction　on　the　disturbances　is　lowered,　the　requirement　for　the　global　information　of　the　communication　topology　is　removed,　and　the　exchanging　information　among　agents　is　only　relative　estimated　states.　Further,　the　output　consensus　performance　is　analyzed　for　the　closed-loop　multi-agent　system.　Our　results　complement　and　improve　the　results　of　the　existing　literature.　Lastly,　the　effectiveness　and　superiority　of　the　developed　method　are　demonstrated　through　a　numerical　simulation　and　a　comparison　with　the　distributed　extended-state-observer-based　method.　IEEE