The quantum double model can be generalized to the case where the input data is given by a C* Hopf algebra. In this case, the face and vertex operators are constructed using the comultiplication of Hopf algebra. For each vertex, the Haar integral of the input Hopf algebra is used to construct the vertex operator. For each face, the Haar integral of the dual Hopf algebra of the input Hopf algebra is used to construct the face operator.