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In a previous paper by the authors, we obtain the first example of a finitelyfreely generated simple $\mathbb Z$-graded Lie conformal algebra of lineargrowth that cannot be embedded into any general Lie conformal algebra. In thispaper, we obtain, as a byproduct, another class of such Lie conformal algebrasby classifying $\mathbb Z$-graded simple Lie conformal algebras ${\calG}=\oplus_{i=-1}^\infty{\cal G}_i$ satisfying the following, (1) ${\calG}_0\cong{\rm Vir}$, 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 Lieconformal algebras of Block type.

Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras