A Fully Affine Invariant Feature (FAIF) detector based on affine Gaussian scale-space has been put forward. Affine Gaussian scale-space is difficult to be built up. FAIF transforms the affine Gaussian scale-space into scale space to cope with the complexity of affine Gaussian scale-space construction. Covariance matrix of an image patch is used to measure the isotropy of the patch. Anisotropic patches are transformed into isotropic ones by rotating and squeezing. Finally, the fully affine invariant key points are detected on isotropic patches. Experimental results indicate that FAIF has the ability to cope with large view angle and scale changes. Moreover, sufficient matches have been detected by FAIF even in images of 3D scenes. Compared with the state- of- the- art, FAIF is the best.