a method and an apparatus for growing a crystal of a compound semiconductor , in which a heater , used to heat a boat for growing the semiconductor crystal , is disposed around an ampule containing the boat , and a melt of the compound semiconductor , which is prepared in the boat , is freezed gradually at a predetermined temperature gradient including the freezing point of the melt , from a crystal growth starting end of the boat to a crystal growth terminating end thereof , whereby a single crystal or a polycrystal is grown . at the start of crystal growth , a crystalline nucleus is formed by periodically changing the temperature of the crystal growth starting end of the boat , in descending and ascending modes , within a temperature range lower than the melting point of the compound semiconductor , after once lowering the temperature of the starting end to a level lower than the melting point by means of a heater block opposed to the starting end . the crystal is grown around the crystalline nucleus formed in this manner . preferably , the temperature change at the crystal growth starting end is slower in the descendng mode than in the ascending mode . the method of the invention may be applied without regard to the use of a seed crystal .