  The problem on estimate of the Koebe radius for univalent harmonic mappings
of the unit disk $\mathbb D=\{z\in\mathbb C : |z|<1\}$ is considered. For a
subclass of harmonic mappings with the standard normalization and a certain
growth estimate for analytic dilatation, we provide new estimate for the Koebe
radius. New estimate for Taylor coefficients of the holomorphic part of a
function from the subclass under consideration is obtained as a corollary.
