Theκ-deformed extended Galilei Hopf group algebra, Funκ(G (m) ), is introduced. It provides an explicit example of a deformed group with cocycle bicrossproduct structure, and is shown to be the contraction limit of a pseudoextension of the κ-Poincaré group algebra. The possibility of obtaining another deformed extended Galilei groups is discussed, including one obtained from a non-standard Poincaré deformation.