  In this paper, we first introduce the notion of Hom-left-symmetric conformal
bialgebras and show some nontrivial examples.
  Also, we present construction methods of matched pairs of Hom-Lie conformal
algebras and Hom-left-symmetric conformal algebras. Finally, we prove that a
finite Hom-left-symmetric conformal bialgebra is free as a
$\mathbb{C}[\partial]$-module is equivalent to a Hom-parak\"{a}hler Lie
conformal algebra. In particular, we investigate the coboundary
Hom-left-symmetric conformal bialgebras.
