Two coupled dark solitons are considered in a two-component Bose-Einstein condensate.and their dynamics are investigated by the variational approach based the renormalized integrals of motion.The stationary states as physical solutions to the describing equations are obtained,and the dynamic mechanism is demonstrated by performing a coordinate of a classical particle moving in an effective potential field.The switching and selftrapping dynamics of the coupled dark vector solitons are discussed by the evolution of the atom population transferring ratio.