We theoretically study the spin-dependent transport in a ferromagnet/superconductor/ferromagnet double tunnel junction. The tunneling current in the antiferromagnetic alignment of the magnetizations gives rise to a spin imbalance in the superconductor. The resulting nonequilibrium spin density strongly suppresses the superconductivity with increase of bias voltage and destroys it at a critical voltage ${V}_{c}$. The results provide a new method not only for measuring the spin polarization of ferromagnets but also for controlling superconductivity and tunnel magnetoresistance by applying a bias voltage.