We have investigated the thickness dependence of magnetic anisotropy and intrinsic anomalous Hall effect (AHE) in single-crystalline full-Heusler alloy Co2MnAl (CMA) grown by molecular-beam epitaxy on GaAs(001). The magnetic anisotropy is the interplay of uniaxial and the fourfold anisotropy, and the corresponding anisotropy constants have been deduced. Considering the thickness of CMA is small, we ascribe it to the influence from interface stress. The AHE in CMA is found to be well described by a proper scaling. The intrinsic anomalous conductivity is found to be smaller than the calculated one and is thickness dependent, which is ascribed to the influence of chemical ordering by affecting the band structure and Fermi surface.