We prove Conjecture 1.1 in [Chan-Lau-Leung] for toric Calabi-Yau manifolds of
the form $K_Y$ where $Y$ is a toric Fano manifold. In particular, we show that
the coefficients of the Taylor series expansions of the inverse mirror map for
$K_Y$ can be expressed in terms of disk open Gromov-Witten invariants defined
by Fukaya-Oh-Ohta-Ono.