Magnetocrystalline anisotropy (MCA) is one of the key parameters investigated in spin-based electronics (spintronics), e.g. for memory applications. Here, we employ first-principles calculations to study MCA in thin film full Heusler alloy Co2CrAl. This material was studied in the past, and has been reported to exhibit half-metallic electronic structure in bulk geometry. In our recent work, we showed that it retains a 100% spin-polarization in thin-film geometry, at CrAl atomic surface termination. Here, we show that the same termination results in a perpendicular magnetic anisotropy, while Co surface termination not only destroys the half-metallicity, but also results in in-plane magnetization orientation. In addition, for films thicker than around 20 nm the contribution from magnetic shape anisotropy may become decisive, resulting in in-plane magnetization orientation. To the best of our knowledge, this is one of the first reports of half-metallic thin-film surfaces with perpendicular magnetic anisotropy. This result may be of interest for potential nano-device applications, and may stimulate a further experimental study of this and similar materials.