  Let $X\subseteq \mathbb{P}^N$ be a non-degenerate normal projective variety
of codimension $e$ and degree $d$ with isolated $\mathbb{Q}$-Gorenstein
singularities. We prove that the Castelnuovo-Mumford regularity
$\text{reg}(\mathcal{O}_{X})\le d-e$, as predicted by the Eisenbud-Goto
regularity conjecture. Such a bound fails for general projective varieties. The
main techniques are Noma's classification of non-degenerated projective
varieties and Nadel vanishing for multiplier ideals. We also classify the
extremal and the next to extremal cases.
