  In this paper, we first determine Bohr's inequality for the class of harmonic
mappings $f=h+\overline{g}$ in the unit disk $\ID$, where either both
$h(z)=\sum_{n=0}^{\infty}a_{pn+m}z^{pn+m}$ and
$g(z)=\sum_{n=0}^{\infty}b_{pn+m}z^{pn+m}$ are analytic and bounded in $\ID$,
or satisfies the condition $|g'(z)|\leq d|h'(z)|$ in $\ID\backslash \{0\}$ for
some $d\in [0,1]$ and $h$ is bounded. In particular, we obtain Bohr's
inequality for the class of harmonic $p$-symmetric mappings. Also, we
investigate the Bohr-type inequalities of harmonic mappings with a multiple
zero at the origin and that most of results are proved to be sharp.
