A semi-synchronous circuit is a circuit in which every register is ticked by a clock periodically, but not necessarily simultaneously. A feature of semi-synchronous circuits is that the minimum delay between registers may be critical with respect to the clock period of the circuit. In this paper, we discuss a delay insertion method which makes such a semi-synchronous circuit faster. The maximum delay-to-register ratio of the cycles on the circuit gives a lower bound of the clock period. We show that this bound is achieved in the semi-synchronous framework by the proposed gate-level delay insertion method on the assumption that the delay of each element on the circuit is unique.