Thin Co films with varying thickness from 1 to 8 monolayers (ML) are epitaxially grown on Pd(001) and are studied in situ by using reflection high-energy electron diffraction (RHEED), scanning tunneling microscope (STM), low-energy electron diffraction (LEED), and magneto-optical Kerr effect (MOKE). The films take the layer-by-layer growth mode up to 3ML, and then switch to the 3dimensional growth mode afterward. For the as-grown films, MOKE measurements show that the easy axis of magnetism is in-plane and the interfacial Pd layer is magnetized. These results are confirmed and explained by density functional calculations.