The β -dual of a vector-valued sequence space is defined and studied. We show that if an X -valued sequence space E is a BK-space having AK property, then the dual space of E and its β -dual are isometrically isomorphic. We also give characterizations of β -dual of vector-valued sequence spaces of Maddox ℓ ( X , p ) , ℓ ∞ ( X , p ) , c 0 ( X , p ) , and c ( X , p ) .