The structural, magnetic, and magnetocaloric properties of epitaxial Ni-Co-Mn-Al thin films with different compositions have been studied. The films were deposited on MgO(001) substrates by co-sputtering on heated substrates. All films show a martensitic transformation, where the transformation temperatures are strongly dependent on the composition. The structure of the martensite phase is shown to be 14M. The metamagnetic martensitic transformation occurs from strongly ferromagnetic austenite to weakly magnetic martensite. The structural properties of the films were investigated by atomic force microscopy and temperature dependent x-ray diffraction. Magnetic and magnetocaloric properties were analyzed using temperature dependent and isothermal magnetization measurements. We find that Ni41Co10.4Mn34.8Al13.8 films show giant inverse magnetocaloric effects with magnetic entropy change of 17.5 J kg(-1) K-1 for mu(0)Delta H = 5 T.