We consider the following coupled Schr$ \ddot{o} $dinger system with critical exponent in $ \mathbb{R}^3: $$ \left \{ \begin{aligned} &-\Delta u+\lambda V(|y|)u = K_1(|y|)u^5+u^2v^3,\qquad &\text{ in } \mathbb{R}^3\backslash B_\epsilon(0),\\ &-\Delta v+\lambda V(|y|)v = K_2(|y|)v^5+v^2u^3, \qquad &\text{ in } \mathbb{R}^3\backslash B_\epsilon(0),\\ &u >0, v>0, \quad &\text{ in } \mathbb{R}^3\backslash B_\epsilon(0), \\ & (u,v) = (0,0), \quad &\text{on } \partial B_\epsilon (0), \\ &u,v\in D^{1,2}(\mathbb{R}^3\backslash B_\epsilon(0))), \end{aligned} \right. $where $ V(|y|) $ is the potential function satifying $ 0<V(|y|)\leq C\frac{1}{(1+|y|)^4} $ in $ \mathbb{R}^3\backslash B_\epsilon(0), $ $ \lambda>0 $ is a constant. $ K_i ( i = 1,2 ) $ are smooth bounded functions satisfying some suitable assumptions. $ B_\epsilon(0) $ is the ball centered at the origin with radius $ \epsilon. $ By using Schmidt reduction arguments combine with the energy expansion and the critical point theory, we prove the existence of infinitely nonradial solutions for the system.