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