We present measurements of the spin and orbital magnetic moments of Fe3O4 by using SQUID and magnetic circular dichroism in soft x-ray absorption. The measurements show that Fe3O4 has a noninteger spin moment, in contrast to its predicted half-metallic feature. Fe3O4 also exhibits a large unquenched orbital moment. Calculations using the local density approximation including the Hubbard U method and the configuration interaction cluster-model suggest that strong correlations and spin-orbit interaction of the 3d electrons result in the noninteger spin and large orbital moments of Fe3O4.