The nonequilibrium Kondo effect is studied in a molecule quantum dot coupled asymmetrically to two ferromagnetic electrodes by employing the nonequilibrium Green function technique.The current-induced deformation of the molecule is taken into account,modeled as interactions with a phonon system,and phonon-assisted Kondo satellites arise on both sides of the usual main Kondo peak.In the antiparallel electrode configuration,the Kondo satellites can be split only for the asymmetric dot-lead couplings,distinguished from the parallel configuration where splitting also exists,even though it is for symmetric case.We also analyze how to compensate the splitting and restore the suppressed zero-bias Kondo resonance.It is shown that one can change the TMR ratio significantly from a negative dip to a positive peak only by slightly modulating a local external magnetic field,whose value is greatly dependent on the electron-phonon coupling strength. The nonequilibrium Kondo effect is studied in a molecule quantum dot coupled asymmetrically to two ferromagnetic electrodes by employing the nonequilibrium Green function technique. Current-induced deformation of the molecule is taken into account, modeled as interactions with a phonon system, and phonon-assisted Kondo satellites arise on both sides of the usual main Kondo peak. In the antiparallel electrode configuration, the Kondo satellites can be split only for the asymmetric dot-lead couplings, distinguished from the parallel configuration where splitting also exists, even though it is for symmetric case.We also analyze how to make the splitting and restore the suppressed zero-bias Kondo resonance. It can be that the one can change the TMR ratio significantly from a negative dip to a positive peak only by slightly modulating a local external magnetic field, whose value is greatly dependent on the electron-phonon coupling strength.