The rhythmic visual stimulation (RVS)-induced oscillatory brain responses, namely steady-state visual evoked potentials (SSVEPs), have been widely used as a biomarker in studies of neural processing based on the assumption that they would not affect cognition. However, recent studies have suggested that the generation of SSVEPs might be attributed to neural entrainment and thus could impact brain functions. But their neural and behavioral effects are yet to be explored. No study has reported the SSVEP influence on functional cerebral asymmetry (FCA). We propose a novel lateralized visual discrimination paradigm to test the SSVEP effects on visuospatial selective attention by FCA analyses. Thirty-eight participants covertly shifted their attention to a target triangle appearing in either the lower-left or -right visual field (LVF or RVF), and judged its orientation. Meanwhile, participants were exposed to a series of task-independent RVSs at different frequencies, including 0 (no RVS), 10, 15, and 40-Hz. As a result, it showed that target discrimination accuracy and reaction time (RT) varied significantly across RVS frequency. Furthermore, attentional asymmetries differed for the 40-Hz condition relative to the 10-Hz condition as indexed by enhanced RT bias to the right visual field, and larger Pd EEG component for attentional suppression. Our results demonstrated that RVSs had frequency-specific effects on left–right attentional asymmetries in both behavior and neural activities. These findings provided new insights into the functional role of SSVEP on FCAs.