  In this paper, we study the Ext-algebras of graded skew extensions. For a
connected graded algebra $A$ and a graded automorphism $\sigma$, we analyze the
Yoneda product of the Ext-algebra of graded skew extension $A[z;\sigma]$, and
prove this Ext-algebra is an $R$-smash product of the Ext-algebra of $A$ and
the one of polynomial algebra $k[z]$ as an associative algebra.
