Drinfeld gave a current realization of the quantum affine algebras as
a Hopf algebra with a simple comultiplication for the quantum current
operators. In this Letter, we will present a generalization of such a
realization of quantum Hopf algebras. As a special case, we will choos
e the structure functions for this algebra to be elliptic functions to
derive certain elliptic quantum groups as a Hopf algebra, which degen
erates into quantum affine algebras if we take certain degeneration of
the structure functions.