In this paper, we propose a higher order and high resoltuion approach for the simulation of magnetized electrons in quasi-neutral plasmas by hyperbolic method. Numerical fluxes for diffusion are constructed by a low dissipation upwind scheme via an equivalent hyperbolic system in steady state. We demonstrated that by using higher order finite difference weighted compact non-linear scheme (WCNS) for diffusion terms the numerical viscosity arising due to anisotropic diffusion can be drastically improved. Numerical results presented here not only demonstrated higher order accuracy but also accelerated steady convergence compared to the traditional second order schemes. The difference between computed transverse electron fluxes by HES and MFAM approach are 4% on the coarsest mesh and reduces to 0.2% by mesh refinement.