The spin-dependent polaron dynamics in organic ferromagnets under driven electric fields are investigated by using the extended Su-Schrieffer-Heeger (SSH) model coupled with a nonadiabatic dynamics method. It is found that the spin-down polaron with the same spin orientation as the radicals drifts faster than the spin-up one under the same driven electric field. In an applicable range of driven electric fields, the velocity of the spin-down polaron is about 3.4 times that of the spin-up one. The dynamical property of the polaron with each spin (up or down) is asymmetric upon the reversal of the driven electric fields. The diverse dynamical properties of polarons with specific spins can be attributed to the spin nondegenerate polaron energy levels, the dipole moment generated by the asymmetrical polaron charge distributions and the strong electron-lattice coupling in organic ferromagnets. Our findings are expected to be useful for improving organic ferromagnet based spintronic devices.