Co/Pt multilayers with perpendicular anisotropy were deposited using a dc magnetron sputtering system under high vacuum. Magnetization process was investigated by the measurement of magnetic components parallel and perpendicular to the applied field. A dependence of the coercivity of Co/Pt multilayers on the Co layer thickness was reported, in which the total thickness of Co layers kept constant. It is observed that the coercivity increases with the increment of Co layer thickness. For the samples with the same Co layer thickness while different total Co layer thickness, the coercivity first increases and then decreases with the increase of the total thickness of Co layers. This effect could be attributed to the competition between the reduction of HC related to incoherent reversal and the step-up of HC contributed by the magnetic polarization of Pt atoms at the interface of Co and Pt layers during magnetization reversal. The results show that the change of the coercivity is strongly related to the Co layer thickness, but not the total thickness of Co layers. The dependence of the coercivity on the angle between an applied field and the easy axis shows that the nucleation mode is dominant in magnetization reversal process of the samples.