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Eight possible native point defects in Mg24Y5 are studied from the density functional theory (DFT) calculations within GGA approximation. The energetic results show that anti-site defects with lower formation energies are energetically favored over vacancies. Under both Mg-rich and Y-rich conditions, MgY1 defect is dominant due to the lowest defect formation energy, followed by YMg2, MgY2 and YMg1, which reasonably explains the Mg-rich off-stoichiometry of Mg24Y5 alloys. For vacancy defects, the formation energies on the two Mg sub-lattices are smaller than ones on two Y sub-lattices, and VMg1 has the lowest formation energy, while VY2 is most unlikely due to the highest formation energy originating from the large mismatch in atomic size and the strong interaction of Y with surrounding atoms. The defect concentration distribution as a function of temperature and stoichiometry is further obtained from grand canonical statistics. The size factor and electronic structure are further discussed, demonstrating that Mg24Y5 alloy is typical system in which the point defects are affected by strong size effect due to the large atomic size radius and strong electronic factor caused by the intensive interaction of Y with the surrounding atoms.