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In this paper, we classify all finite irreducible conformal modules over aclass of Lie conformal algebras $\mathcal{W}(b)$ with $b\in\mathbb{C}$ relatedto the Virasoro conformal algebra. Explicitly, any finite irreducible conformalmodule over $\mathcal{W}(b)$ is proved to be isomorphic to$M_{\Delta,\alpha,\beta}$ with $\Delta\neq 0$ or $\beta\neq 0$ if $b=0$, or$M_{\Delta,\alpha}$ with $\Delta\neq 0$ if $b\neq0$. As a byproduct, all finiteirreducible conformal modules over the Heisenberg-Virasoro conformal algebraand the Lie conformal algebra of $\mathcal{W}(2,2)$-type are classified.Finally, the same thing is done for the Schr\"odinger-Virasoro conformalalgebra.

Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal algebra