  Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of
Virasoro Lie conformal algebra and its nontrivial conformal modules of rank
one. In this paper, we give a complete classification of extensions of finite
irreducible conformal modules of $\mathcal{W}(a,b)$. With a similar method, we
characterize all extensions of finite irreducible conformal modules of
Schr\"{o}dinger-Virasoro type Lie conformal algebras $TSV(a,b)$ and $TSV(c)$.
