The problem on estimating 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 a new estimate for the Koebe radius. A new estimate for Taylor coefficients of the holomorphic part of a function from the subclass under consideration is obtained as a corollary.
