In this paper, we study the existence and multiplicity of positive nontrivial solutions of the following singular fractional elliptic system \begin{equation*} \begin{cases} (-\Delta)^s_pu=a(x)u^{-\gamma}+ambda f(x,u,v)ext{ in }mega, (-\Delta)^s_pv=b(x)v^{-\gamma}+ambda g(x,u,v)ext{ in }mega, u=v=0ext{ on } \mathbb R^N\backslash mega, \end{cases} \end{equation*} where $\Omega$ is a smooth bounded domain in $\mathbb R^N$, $N>ps$ with $s\in(0,1)$, $\lambda$ is a positive parameter and $0<\gamma<1<p<r<p^*_s-1$, $p^*_s=\frac{Np}{N-ps}$. $a,b\in L^\infty(\Omega,\mathbb R^+_*)$, $f,g\in C(\Omega\times\mathbb R\times\mathbb R,\mathbb R^+)$ are positively homogeneous functions of degree $(r-1)$. The results are obtained by using the fibering method, Nehari Manifold technique and applying Ekeland's variational principle.