Abstract: Let $\mathscr{C}$ be an abelian category with enough projectives and injectives and let ($\mathscr{A}$,$\mathscr{B}$) be a complete hereditary cotorsion pair in $\mathscr{C}$. The definition and equivalent characterizations of Gorenstein $\mathscr{A}-\mathscr{B}$ objects in abelian category $\mathscr{C}$ are given. Additionally, the related properties of Gorenstein $\mathscr{A}-\mathscr{B}$ dimensions in module category are studied.

Key words: cotorsion pair, Gorenstein $\mathscr{A}-\mathscr{B}$ object, Gorenstein $\mathscr{A}-\mathscr{B}$ dimension