The hydrodynamic formulation of mixed quantum states involves a hierarchy of coupled equations of motion for the momentum moments of the Wigner function. In this work a closure scheme for the hierarchy is developed. The closure scheme uses information contained in the lower known moments to expand the Wigner phase-space distribution function in a Gauss-Hermite orthonormal basis. The higher moment required to terminate the hierarchy is then easily obtained from the reconstructed approximate Wigner function by a straightforward integration over the momentum space. Application of the moment closure scheme is demonstrated for the dissipative and nondissipative dynamics of two different systems: (i) double-well potential, (ii) periodic potential.