An effective, simple and low-cost a method for growing single crystals of perovskite oxideshaving primary and secondary abnormal grain growths according to temperature condition higher than a determined temperature or an atmosphere of heat treatment, involves a perovskite seed single crystal being adjoined to a polycrystal of perovskite oxides and heating the adjoined combination whereby the seed single crystal grows into the polycrystal at the interface therebetween repressing secondary abnormal grain growths inside the polycrystal. 1) The composition ratio of the polycrystal is controlled and/or the specific component(s) of the polycrystal is(are) added in an excess amount compared to the amount of the component(s) of the original composition of the polycrystal, 2) the heating is performed in the temperature range which is over primary abnormal grain growths completion temperature and below secondary abnormal grain growths activation temperature, whereby the seed single crystal grows continuously.