The radioactive decay of Ga-72 has been; investigated by means of NaI-HpGe Compton-suppress spectrometer, and gamma-gamma coincidence measurements performed with two HpGe detectors coupled to three-parameter (gamma-gamma-T) data acquisition system. 2.3 x 10(7) coincidence events are collected. A new decay scheme of Ga-72 including 26 levels,87 gamma-rays is established. The extensive coincidence relationships are used to identify the gamma-rays and levels of Ge-72, such as new gamma-rays of 225.92, 826.97, 1349.71, 1475.32, 1667.91, 2105.28, 2247.39 keV and new levels of 3248.01, 3396.27, 3806.10, 3864.56 keV. The unsure transitions of 112.59, 937.97, 2402.25, 2939.95 keV and level of 2939.83 keV are confirmed in this work. No evidence has been observed for the existences of 113.5, 1155.7, 1192.4 keV gamma-rays and level of 3707.1 keV. The transition of 317.72 keV gamma-ray is moved from 3757.26-3439. 51 keV level to 3565.85-3248.01 keV level.