  This paper deals with the existence of positive solution for the singular
quasilinear Schr\"odinger equation $-\Delta u -\Delta (u^{2})u=h(x) u^{-\gamma}
+ f(x,u)~\mbox{in} ~ \Omega,$ where $\gamma > 1$, $\Omega \subset
\mathbb{R}^{N}, (N\geq 3)$ is a bounded smooth domain, $0<h\in L^{1}(\Omega)$,
$f$ is a measurable function that can change signal and can be sublinear or has
critical growth. Inspired by Sun \cite{Y} we derive a compatible condition on
the couple $(h(x),\gamma)$, which is optimal for the existence of
$H_{0}^{1}$-solution for this problem.
