  In this paper, we study the Pohozaev identity associated with a
H$\acute{e}$non-Lane-Emden system involving the fractional Laplacian:
  \begin{equation}
  \left\{\begin{array}{ll}
  (-\triangle)^su=|x|^av^p,&x\in\Omega,
  (-\triangle)^sv=|x|^bu^q,&x\in\Omega, u=v=0,&x\in R^n\backslash\Omega,
  \end{array}
  \right.
  \end{equation} in a star-shaped and bounded domain $\Omega$ for $s\in(0,1)$.
As an application of our identity, we deduce the nonexistence of positive
solutions in the critical and supercritical cases.
