Under the assumption that clock can be inputted to each register at an arbitrary timing, the minimum feasible clock period can be determined if delays between registers are given. This minimum feasible clock period might be reduced if delays between some registers are increased by delay insertion. In this paper, we propose a delay insertion algorithm to reduce the minimum clock period. First, the proposed algorithm determines a clock schedule ignoring some constraints. Second, the algorithm inserts delays to recover ignored constraints according to the delay-slack and delay-demand of the obtained clock schedule. We show that the proposed algorithm achieves the minimum clock period by delay insertion if the delay of each element in the circuit is unique. Experiments show that the amount of inserting delay and computational time are smaller than the conventional algorithm.