  In this second paper on loop quantization of Gowdy model, we introduce the
kinematical Hilbert space on which appropriate holonomies and fluxes are well
represented. The quantization of the volume operator and the Gauss constraint
is straightforward. Imposition of the Gauss constraint can be done on the
kinematical Hilbert space to select subspace of gauge invariant states. We
carry out the quantization of the Hamiltonian constraint making specific
choices. Alternative choices are briefly discussed. It appears that to get
spatial correlations reflected in the Hamiltonian constraint, one may have to
adopt the so called `effective operator viewpoint'.
