  In this paper, we derive the quantum hydrodynamics models based on the moment
closure of the Wigner equation. The moment expansion adopted is of the Grad
type firstly proposed in \cite{Grad}. The Grad's moment method was originally
developed for the Boltzmann equation. In \cite{Fan_new}, a regularization
method for the Grad's moment system of the Boltzmann equation was proposed to
achieve the globally hyperbolicity so that the local well-posedness of the
moment system is attained. With the moment expansion of the Wigner function,
the drift term in the Wigner equation has exactly the same moment
representation as in the Boltzmann equation, thus the regularization in
\cite{Fan_new} applies. The moment expansion of the nonlocal Wigner potential
term in the Wigner equation is turned to be a linear source term, which can
only induce very mild growth of the solution. As the result, the local
well-posedness of the regularized moment system for the Wigner equation remains
as for the Boltzmann equation.
