Let $(X,L)$ be a quasi-polarized canonical Calabi–Yau threefold. In this note, we show that $\vert mL\vert $ is basepoint free for $m\ge 4$. Moreover, if the morphism $\Phi _{\vert 4L\vert }$ is not birational onto its image and $h^0(X,L)\ge 2$, then $L^3=1$. As an application, if $Y$ is an $n$-dimensional Fano manifold such that $-K_Y=(n-3)H$ for some ample divisor $H$, then $\vert mH\vert $ is basepoint free for $m\ge 4$ and if the morphism $\Phi _{\vert 4H\vert }$ is not birational onto its image, then either $Y$ is a weighted hypersurface of degree $10$ in the weighted projective space $\mathbb{P}(1,\dots ,1,2,5)$ or $h^0(Y,H)=n-2$.