For any gentle algebra $Lambda=KQ/langle Irangle$, following Kalck, we describe the quiver and the relations for its Cohen-Macaulay Auslander algebra $mathrm{Aus}(mathrm{Gproj}Lambda)$ explicitly, and obtain some properties, such as $Lambda$ is repre
sentation-finite if and only if $mathrm{Aus}(mathrm{Gproj}Lambda)$ is; if $Q$ has no loop and any indecomposable $Lambda$-module is uniquely determined by its dimension vector, then any indecomposable $mathrm{Aus}(mathrm{Gproj}Lambda)$-module is uniquely determined by its dimension vector.
Let $K$ be an algebraically closed field. Let $(Q,Sp,I)$ be a skewed-gentle triple, $(Q^{sg},I^{sg})$ and $(Q^g,I^{g})$ be its corresponding skewed-gentle pair and associated gentle pair respectively. It proves that the skewed-gentle algebra $KQ^{sg}
/< I^{sg}>$ is singularity equivalent to $KQ/< I>$. Moreover, we use $(Q,Sp,I)$ to describe the singularity category of $KQ^g/< I^g>$. As a corollary, we get that $mathrm{gldim} KQ^{sg}/< I^{sg}><infty$ if and only if $mathrm{gldim} KQ/< I><infty$ if and only if $mathrm{gldim} KQ^{g}/< I^{g}><infty$.
