  This paper is devoted to study the nonexistence results of positive solutions
for the following fractional H$\acute{e}$non system \begin{eqnarray*}\left\{
\begin{array}{lll}
  &(-\triangle)^{\alpha/2}u=|x|^av^p,~~~&x\in R^n,
  &(-\triangle)^{\alpha/2}v=|x|^bu^q,~~~ &x\in R^n,
  &u\geq0, v\geq 0,
  \end{array}
  \right. \end{eqnarray*} where $0<\alpha<2$, $0<p,q<\infty$, $a$, $b$ $\geq0$,
$n\geq2$. Using a direct method of moving planes, we prove non-existence of
positive solution in the subcritical case.
