Based on imaginary time propagation method, we realize the Wigner ground state calculation. Since Wigner function is a high dimensional phase space function, appropriate spectral methods are introduced to reduce the dimensionality and to handle the global operators. Firstly, with the aid of the governing equation in Schrödinger imaginary time propagation method, governing equation of Wigner version is derived. Then, according to the expression of the convolution term in the equation, discretization methods of momentum space are designed with simplified Grad moment method and Fourier pseudo-spectral method, respectively. Corresponding numerical details are discussed. In particular, we consider density functional theory calculation in the framework of our methods. A reconstruction method of high order derivative of density is proposed for simplified Grad moment method. Several numerical experiments demonstrate validity of our methods and the potential in many-body problems.