We propose a new method to propagate a quantum wavepacket based on a phase space approach.This approach employs the periodic von Neumann basis with biorthogonal exchange (pvb basis), which has recently been introduced and developed for the calculation of energy eigenstates of quantum systems [1].In the pvb basis, generated from a lattice of phase space Gaussians with periodic boundary conditions, a quantum state can be represented accurately by a small subset of the basis selected based on phase space structure of the corresponding classical mechanical system.