Co films with thickness ranging from 20 to 160 nm have been fabricated on SiO2/Si substrates by pulsed laser deposition method (PLD). It was found that that the Co crystal tends to have a structure of bulk hcp Co with the increase of the Co film thickness, and the coercivity of the Co film decreases with increasing film thickness due to the change of the grain size. A uniaxial anisotropy was found in Co films with thickness less than 120 nm, while the Co films with thickness more than 120 nm show an unexpected four-fold anisotropy which is ascribed to the existence of two types (directions) of strongly exchange-coupled hcp Co grains.