A clock design apparatus includes a delay time adjusting section, a prohibition specifying section and a clock tree synthesis section. The delay time adjusting section is configured to adjust signal delay time of signal propagation paths on a semiconductor integrated circuit to be designed. The prohibition specifying section is configured to specify a part of the signal propagation paths as a circuit prevented from being changed. The clock tree synthesis section is configured to synthesize a clock tree of the semiconductor integrated circuit in accordance with the specification made by the prohibition specifying section.