A new generalization of normality called almost $\beta$-normality is introduced and studied which is a simultaneous generalization of almost normality and $\beta$-normality. A topological space is called almost $\beta$-normal if for every pair of disjoint closed sets $A$ and $B$ one of which is regularly closed, there exist disjoint open sets $U$ and $V$ such that $\overline{U\cap A}=A$, $\overline{U\cap B}=B$ and $\bar U\cap\bar V=\phi$.