  Let $k$ and $n$ be positive even integers. For a Hecke eigenform $h$ in the
Kohnen plus subspace of weight $k-n/2+1/2$ for $\varGamma_0(4)$, let $I_n(h)$
be the Duke-Imamoglu-Ikeda lift of $h$ to the space of cusp forms of weight $k$
for $Sp_n(\mathbb Z)$. We then give an estimate of the Fourier coefficients of
$I_n(h)$. It is better than the usual Hecke bound for the Fourier coefficients
of a Siegel cusp form.
