The controllability of charge transport through an organic molecular spin-valve system is theoretically investigated on the basis of a Su-Schrieffer-Heeger model combined with the non-equilibrium Green's function formalism. We show how the formation of polaron in the organic sub-structure leads to a hysteretic conductance switching, via sweeping either the bias voltage or the electrochemical potential. We further obtain an exponential dependence of the magnetoresistance as a function of the applied bias voltage. The implications of calculated results in relation to experiments and device applications are addressed and commented.