The periodic transcription output is ubiquitously observed in an isogenic cell population. To understand mechanisms of cyclic behavior in transcription, we extend the gene activation process in the two-state model by assuming the synthesis rate is periodic. We derive the analytical forms of the mean transcript level and the noise. The limits of them indicate the mean level and the noise display periodic behaviors. Our numerical examples strongly suggest that the transcription system with a periodic synthesis rate generates more noise than that with a constant rate, but maintains transcription homeostasis in each period. It also suggests that if the periodicity is not considered, the calculated noise may be greater than the correct value.