This work addresses the effect of anisotropic pressure on the strong magnetized white dwarf. A quasi-local equation of state is used to formulate the anisotropic factor inside the star. We use the assumption that the magnetic field is constant and strong enough to make degenerate electrons very energetic and occupy the first Landau level. Modified Lane-Emden equation is formulated and solved numerically. We interested in magnetized white dwarfs with mass range M=2.1-2.8 M_⨀ that was predicted as a progenitor for a peculiar type Ia-supernovae, which are characterized by low kinetic energy and over luminosities. In a good approximation, a mass-radius relation for this range of star masses was determined. It is found that the mass and radius of the stars increase due to anisotropic effect. The radius of the star decreases with increasing maximum energy of degenerate electrons and magnetic field intensity, which indicates that these quantities support occurrence of the explosion. The main disadvantage of used model is that the predicted internal magnetic field strength exceeds the maximum magnetic field needed for star stability, which refers that these stars are unstable and unbound.