A weak solution based particle flow filter is proposed for the difficulties of particle velocity field computation existed in the present particle flow filter. By regarding the particle velocity field as the gradient of the potential function, a weak formulation of partial differential equation(PDE) in which the velocity field is satisfied is derived. Subsequently, a weak solution with low computation is derived by using Galerkin method and Monte-Carlo integral. Simulation results show that local convergence of Gaussian approximation based filter occurs under certain initial conditions whereas the particle flow filter is nevertheless effective, with preferable tracking accuracy and robustness.