In this paper, we study the positive solutions of higher order Lane-Emden system with Navier exterior conditions $$ \begin{cases} \ (-\Delta)^{s}u(x)=v^{p}(x) ,\ u(x)>0,\qquad \ x\in\Omega,\\ \ (-\Delta)^{s}v(x)=u^{q}(x) ,\ v(x)>0,\qquad \ x\in\Omega,\\ \ u(x)=-\Delta u(x)=\cdot\cdot\cdot=(-\Delta)^{m} u(x)=0,\ x\in\Omega^{c},\\ \ v(x)=-\Delta v(x)=\cdot\cdot\cdot=(-\Delta)^{m} v(x)=0,\ x\in\Omega^{c}, \end{cases} $$ where $1