We observed an anomalously outbursting state of SU UMa which occurred in 1992. Time-resolved photometry revealed the presence of signals with a period of d, which is 3.6σ longer than the orbital period (0.07635 d) of this system. We attributed this signal to superhumps, based on its deviation from the orbital period and its characteristic profile. During this anomalous state of SU UMa, normal outbursts were almost suppressed, in spite of relatively regular occurrences of superoutbursts. We consider that an ensuing tidally unstable state following the preceding superoutburst can be a viable mechanism to effectively suppress normal outbursts, resulting in an anomalously outbursting state.