Abstract: Smooth surface reconstruction from noisy scattered data owns a large application background. A new energy model is proposed to solve this problem based on variational level set methods and a partial differential equation （PDE） is thus deduced.The limit surface obtained by PDE evolution is the reconstructed smooth surface.We provide a fast method to construct the initial surface,which saves the temporal cost of reconstruction.Then level set methods are utilized to solve the initialization problem of the PDE,where we discretize space by essentially non-oscillatory or weighted essentially non-oscillatory technique and discretize time by total variation diminishing （TVD） Runge-Kutta method of high precision.A TVD Runge-Kutta method with varying time steps is proposed to reinitialize the signed distance function,which guarantees the upwind design of each Euler step.The experiments show that the method proposed is efficient and can produce visual pleasing reconstruction results.