Summary: ``In this paper, we study the system of the coupled nonlinear Schrödinger equation in dimension three. By establishing the a priori interaction, Morawetz estimate in the spirit of the work of Tao et al. [The nonlinear Schrödinger equation with combined power-type nonlinearities. Commun. Par. Differ. Equ. 2007;32: 1281--1343] [MR2354495], we prove the global well-posedness and scattering of the solution $(u, v)$ to the defocusing coupled equation. Furthermore, we adapt the standard method from Cazenave [Semilinear Schrödinger equations. Vol. 10, Courant lecture notes in mathematics. Providence (RI): American Mathematical Society; 2003] [MR2002047] to obtain the blowup result for the focusing case under the restriction: energy is negative and the initial data belongs to $\Sigma\coloneq H^1\cap L^2(|x|^2dx)$ or the initial data is radial.''