The high-quality inverse spinel CuCo2O4 thin films are epitaxially grown on (001) MgAl2O4 substrates by radio frequency magnetron sputtering. The electrical transport properties exhibit typical semiconducting characteristics, accompanying the enhancement of resistivity with the thinning of CuCo2O4 thickness. The transport properties could be well understood by the Mott variable range hopping model. The anomalous Hall effect with a clear hysteresis loop is observed below 100 K, indicating the existence of out-of-plane magnetization in the epitaxial-grown CuCo2O4 films. In addition, the negative magnetoresistance at low temperature reverses to the positive magnetoresistance (≥100 K), which is related to the changes from the decrease in spin/carrier scattering under the magnetic field at low temperature to the enhancement of carrier deflection due to the conventional Lorenz force (≥100 K). The observed physical properties are closely related to the orbital occupation of Cu ion in CuCo2O4 films, which is a significant difference compared to that of documented metallic NiCo2O4. This work is a good comprehensive study of inverse spinel oxide thin films.