The hyperbolic-equation-system (HES) approach has been developed for the calculation of magnetized electron fluids in quasi-neutral plasmas. The HES approach has been applied to a particle-fluid hybrid modeling of a Hall thruster, to evaluate the applicability of the approach to practical simulations. The validity of the use of the HES approach is confirmed based on three aspects. First, the calculated thruster performance is in good agreement with the experimental results. Also, it is proven that the two-dimensional conservation law of the electron flow is strictly computed with the HES approach. Lastly, the Boltzmann relation along magnetic lines of force is confirmed, which indicates the effect of magnetic confinement is accurately calculated.