Summary: The efficient conditions guaranteeing the existence of positive \(T\)-periodic solution to the \(p\)-Laplacian-Liénard equation \[\bigl(\phi _{p}\bigl(x'(t)\bigr) \bigr)'+f \bigl(x(t)\bigr)x'(t)+\alpha _{1}(t)g\bigl(x(t)\bigr)= \frac{ \alpha _{2}(t)}{x^{\mu }(t)},\] are established in this paper. Here \(\phi _{p}(s)=|s|^{p-2}s\), \(p>1\), \(\alpha _{1},\alpha _{2}\in L([0,T],{R}) \), \(f\in C({R}_{+},{R})\) (\({R} _{+}\) stands for positive real numbers) with a singularity at \(x=0\), \(g(x)\) is continuous on \((0;+\infty )\), \(\mu\) is a constant with \(\mu >0\), the signs of \(\alpha _{1}\) and \(\alpha _{2} \) are allowed to change. The approach is based on the continuation theorem for \(p\)-Laplacian-like nonlinear systems obtained by R. Manásevich and J. Mawhin [J. Differ. Equations 145, No. 2, 367–393 (1998; Zbl 0910.34051)].