Using a finite element method for elastoplastic dynamic analysis, we examine the effects of a low-velocity fault zone (LVFZ) surrounding a fault on a spontaneous dynamic earthquake rupture. A Mohr-Coulomb failure criterion is used to characterize nonelastic off-fault response to earthquake ruptures. We find that the presence of a LVFZ alters the distribution of off-fault plastic strain and results in larger final slip and larger peak slip velocities on the fault. These effects show a LVFZ-width dependency. A supershear (relative to the shear wave velocity of country rocks) rupture transition is observed with a LVFZ width of 400 m or larger (up to 2 km). The presence of a LVFZ increases the amplitude of ground shaking at stations within the LVFZ and induces high-frequency oscillations at stations within and near the LVFZ.