High-field magnetization measurements have been performed for single-crystalline Ce(Col1-xNix)5 with 0 ≤ x ≤ 0.3 in high magnetic fields of up to 40 T. A metamagnetic transition from the low to the high moment state is observed at 21 T in Ce(Co0.9Ni0.1)5. The Co moment is found to be in the high moment state for CeCo5 and in the low moment state for x ≥ 0.1. The transition of the Co moment state due to Ni substitution produces rapid changes in the spontaneous magnetization, the Curie temperature and the anisotropy constant K1. The mechanism of the metamagnetic transition is discussed, and the local magnetic moments and anisotropy constants of Co on the 3g and 2c sites are estimated. The magnetization anisotropy of Ce(Co1-xNix)5 with O ≤ x ≤ 0.3 is found to be constant and very large.