Let $R=K[x_1,\ldots, x_n]$ be the polynomial ring in $n$ variables over a field $K$, and let $I$ be a monomial ideal of $R$. In this short note, we show that if $I$ is of Veronese-type, then for all positive integers $k$, the powers $I^k$ and the radical $\sqrt{I}$ are sequentially Cohen-Macaulay.
