In this study, the theory of minimum detectable activity concentration(MDAC) for airborne gamma-ray spectrometry(AGS) was derived, and the relationship between the MDAC and the intrinsic efficiency of a scintillation counter, volume, and energy resolution of scintillation crystals, and flight altitude of an aircraft was investigated. To verify this theory, experimental devices based on NaI and CeBr_3 scintillation counters were prepared, and the potassium, uranium, and thorium contents in calibration pads obtained via the stripping ratio method and theory were compared. The MDACs of AGS under different conditions were calculated and analyzed using the proposed theory and the Monte Carlo method. The relative errors found via a comparison of the experimental and theoretical results were less than 4%. The theory of MDAC can guide the work of AGS in probing areas with low radioactivity.