Spin imbalance can lead to suppression of superconductivity. We report the phenomena manifesting this effect under spin-polarized quasiparticle currents in ferromagnet-superconductor-ferromagnet single-electron transistors. The measured superconducting gap as a function of magnetic field reveals a dramatic decrease when the magnetizations of the two leads are misaligned. The effect of suppression increases with increasing source-drain voltage. A comparison with theoretical calculations is presented. This method may render it applicable to control superconductivity at low temperatures within low fields.