  In a previous paper by the authors, we obtain the first example of a finitely
freely generated simple $\mathbb Z$-graded Lie conformal algebra of linear
growth that cannot be embedded into any general Lie conformal algebra. In this
paper, we obtain, as a byproduct, another class of such Lie conformal algebras
by classifying $\mathbb Z$-graded simple Lie conformal algebras ${\cal
G}=\oplus_{i=-1}^\infty{\cal G}_i$ satisfying the following, (1) ${\cal
G}_0\cong{\rm Vir}$, the Virasoro conformal algebra; (2) Each ${\cal G}_i$ for
$i\ge-1$ is a ${\rm Vir}$-module of rank one. These algebras include some Lie
conformal algebras of Block type.
