Abstract: In this paper, we firstly deduced a modified formula for pressure of relativistic electrons in superhigh magnetic fields (SMFs) by introducing the electron Landau level stability coefficient g_n and the Dirac -δ function. Then we discuss the quantum electrodynamics effects of SMFs on the phase space, spin polarization and paramagnetic magnetization of electron gas in strongly magnetized neutron stars. Finally, the lattice mater below the "neutron drop density" in the crust and the ideal n-p-e system in the outer core of neutron stars are selected as representatives, and the effects of SMFs on the equation of state are discussed in detail. It is shown that when the nuclide (A, Z) is converted to (A′, Z′) in the lattice below the "neutron drip-out density" in the neutron star outer crust, the phase transition will occur in a lower density due to the SMF effects, and the total pressure of an ideal n-p-e system will increase with the increase of the magnetic field strength.