  In the present paper, we prove that any finite non-trivial irreducible module
over a rank two Lie conformal algebra $\mathcal{H}$ is of rank one. We also
describe the actions of $\mathcal{H}$ on its finite irreducible modules
explicitly. Moreover, we show that all finite non-trivial irreducible modules
of finite Lie conformal algebras whose semisimple quotient is the Virasoro Lie
conformal algebra are of rank one.
