We report that current-induced ultrafast unipolar switching can be realized by utilizing wavy spin-transfer torque (STT) and out-of-plane polarizer. Two spin-valve structures with normal STT and wavy STT are studied to investigate the effect of wavy STT on ultrafast precessional switching. We find that for the structure with normal STT, only antiparallel (AP)-to-parallel (P) switching occurs in one polarity of current whereas for the structure with wavy STT, both P-to-AP and AP-to-P switchings occur, showing alternative switching patterns as a function of current and pulse width.