Let $(R,\fm)$ be a Cohen-Macaulay local ring of dimension $d$, $C$ a canonical $R$-module and $M$ an almost Cohen-Macaulay $R$-module of dimension $n$ and of depth $t$. We prove that $\Dim\Ext_R^{d-n}(M, C)=n$ and if $n\leq 3$ then $\Ext_R^{d-n}(M, C)$ is an almost Cohen-Macaulay $R$-module. In particular, if $n=d\leq 3$ then $\Hom_R(M,C)$ is an almost Cohen-Macaulay $R$-module. In addition, with some conditions, we show that $\Ext_R^1( M,C)$ is also almost Cohen-Macaulay. Finally, we study the vanishing $\Ext_R^i(\Ext_R^{d-n}(M, C), C)$ and $\Ext_R^i(\Ext_R^{d-t}(M, C), C)$.
