The global exponential synchronization of the nonlinear coupled neural network with an asymmetrical matrix and time-varying delays is investigated in this paper. By exerting only an impulsive controller on the first node in the network, without lose generality, sufficient criteria are derived to guarantee the realization of the exponential synchronization for the network no matter the impulsive effect plays a positive or negative role in the procedure of achieving stable. What's more, we give a numerical simulation to support the validity of the analytical results.