Based on the standard nonlinear Schr dinger equation, the first-order breather solution and its rouge wave limit are obtained with Darboux transform method, and the dynamic characteristics of first-order breather solution are studied. High-order breather solutions of nonlinear Schr dinger equation are obtained by means of recurrence relation of Darboux transformation. And their collision superposition, separation, degeneracy and parallel transmission modes are studied, respectively. Nonlinear Schr dinger equation's rouge wave limit can be obtained when each breather frequency tends to zero. Research results show that the rouge wave's amplitude, number of bumps, order of center peaks and number of surrounding peaks after splitting are related to rouge wave's order.