Singularities of 3-dimensional varieties admitting an ample effective divisor of Kodaira dimension zero

For a normal threefold $X$ with an effective Cartier divisor $H$, which is a minimal model of Kodaira dimension zero, we prove that either $X$ is a generalized cone over $H$, or $X$ has quadruple singularities and $H$ is either a K3 surface, or an Enriques surface.