  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 paper, we study
almost Cohen-Macaulay simplicial complex. Moreover, we characterize the almost
Cohen-Macaulay polymatroidal Veronese type and transversal polymatroidal ideals
and furthermore we give some examples.
