  In this paper, we prove $L^q$-estimates for gradients of solutions to
singular quasilinear elliptic equations with measure data
$$-\operatorname{div}(A(x,\nabla u))=\mu,$$ in a bounded domain
$\Omega\subset\mathbb{R}^{N}$, where $A(x,\nabla u)\nabla u \asymp |\nabla
u|^p$, $p\in (1,2-\frac{1}{n}]$ and $\mu$ is a Radon measure in $\Omega$
