In cyclic prefix (CP)-based transmission systems, if the time duration of the cyclic extension is shorter than the channel impulse response duration, system performance is degraded due to the introduction of intersymbol interference (ISI) and intercarrier interference (ICI). In this paper, we propose a blind beamforming algorithm for single-carrier frequency-division multiple-access (SC-FDMA) systems under insufficient CP scenarios. In addition, we also consider the effects of carrier frequency offsets (CFOs) in the processing schemes. The simulation results are presented by employing an SC-FDMA uplink signal model to illustrate the efficacy of the proposed algorithms.