Airborne three-dimensional (3-D) synthetic aperture radar (SAR) imaging has been getting increasing attentions, because of its application prospects in safe navigation, terrain mapping and etc. Resolution is one of the key parameters of 3-D SAR imaging system, therefore to analyze its 3-D resolutions is necessary and significative. In this paper, we derive the resolutions of airborne 3-D SAR via generalized ambiguity function (GAF), which makes us concentrate on how the resolution is obtained, and the derivation also explains the validity of airborne 3-D SAR imaging. However, the resolutions derived by GAF are in the imaging space, which is not parallel with ground-elevation coordinate system (GECS) when the airborne 3-D SAR works under forward-looking mode. Finally, an approach is proposed to transform 3-D resolutions to GECS, and simulation experiments support the analyses.