A single-molecule magnet (SMM) coupled to two normal metallic electrodes can both switch spin-up and spin- down electronic currents within two different windows of SMM gate voltage. Such spin current switching in the SMM tunnel junction arises from spin-selected single electron resonant tunneling via the lowest unoccupied molecular orbit of the SMM. Since it is not magnetically controlled but all-electrically controlled, the proposed spin current switching effect may have potential applications in future spintronics.