With the help of symbolic computation software Maple,by using the CTE method,a coupled Burgers equation was proved to be CTE solvable.Many interaction solutions among solitons and other types of nonlinear excitations of the coupled Burgers equation were obtained,which include soliton-cnoidal waves,multiple resonant solutions,soliton-error function waves,soliton-rational waves,and soliton-periodic waves.The corresponding graphs of the soliton-cnoidal waves and multiple resonant solutions were presented.