We have conducted a systematic magnetic characterization of a series of Zn1-xCoxO samples with different cobalt composition. The Zn1-xCoxO thin films were epitaxially grown by metal organic chemical vapor deposition (MOCVD) on quartz and ZnO substrates. The Co composition was adjusted by controlling the bubbler temperature and carrier gas flow. The magnetization measurements were performed using a Quantum Design MPMS system, which utilizes a superconducting quantum interference device (SQUID) magnetometer. Magnetic hysteresis curves were observed at 5K which persisted up to 300K, possibly characteristic of ferromagnetic behavior. Temperature dependent magnetization was recorded under both zero-field cooled (ZFC) and field cooled (FC) conditions. Changes of magnetization were observed under ZFC and FC conditions in some samples from 5K up to 300K. Composition-dependent changes in magnetization were also observed among samples with different cobalt doping, indicative of ferromagnetism related directly to cobalt incorporation. Magnetic field dependent magnetization at various temperatures with field up to 5 Tesla suggests the Zn1-xCoxO layers were not paramagnetic.