Large single decagonal quasicrystals of Al-Cu-Co-Ge alloy about 0.8 mm in diameter and 10 mm in length have been obtained by the directional growth technique. The single decagonal quasicrystals show decaprismatic morphology and their perfection was examined by electron diffraction. It was found that the perfection of these single quasicrystals depends on the growth rate during the directional solidification. A high density of mixed dislocations with Burgers vectors b parallel to the tenfold axis and stacking faults with displacement vectors R parallel to the tenfold axis were introduced into the quasicrystals during rapid directional growth. The effects of the temperature gradient and rate of growth on the defect formation during directional growth are discussed.