  Let $\overline{p}(n)$ be the number of overpartitions of $n$, we establish
and give a short elementary proof of the following congruence
\[\overline{p}({{4}^{\alpha }}(40n+35))\equiv 0 \, (\bmod \, 40),\] where
$\alpha ,n $ are nonnegative integers. By letting $\alpha =0$ we proved a
conjecture of Hirschhorn and Sellers. Some new congruences for
$\overline{p}(n)$ modulo 3 and 5 have also been found, including the following
two infinite families of Ramanujan-type congruences: for any integers $n\ge 0$
and $\alpha \ge 1$, \[\overline{p}({{5}^{2\alpha +1}}(5n+1))\equiv
\overline{p}({{5}^{2\alpha +1}}(5n+4))\equiv 0 \, (\bmod \, 5).\]
