The multiferroic Co/Co3O4/PZT composite films are prepared on Pt/Ti/SiO2/Si wafers by sol-gel process combined with pulsed laser deposition method. The phase structures, microstructural topographies and element valence states of the composite films are characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and X-ray photoelectron spectrum (XPS). The ferroelectric, electrical and magnetic properties as well as the magnetoelectric coupling behaviors are measured, and the exchange bias effect and its influence on the magnetoelectric coupling behavior of the composite film are studied systematically. #br#The results show the composite films have well-defined ferroelectric hysteresis loops with a remanent polarization value of ～17 μ C/cm2. The composite film exhibits evidently an exchange bias effect. Typically, a exchange bias field of ～80 Oe is observed at 77 K. Both the exchange bias field and magnetic coercive field increase with reducing the temperature. The exchange bias field increases to 160 Oe when the temperature decreases to 10 K. The XPS results confirm that an about 5 nm-thick CoO layer appears at the Co/Co3O4 interface due to the oxygen diffusion during the preparation, indicating that the exchange bias effect at 77 K is caused by the pinning effect of the antiferromagnetic CoO layer while the exchange bias effect at 10 K originates from the combining effect of antiferromagnetic CoO and Co3O4 layers. #br#The measureflent results of magnetocapacitance versus magnetic field curves at different temperatures show that the composite films have remarkable magnetoelectric coupling properties. The response of capacitance to temperature changes with the variation of external magnetic field. Further investigations show that the composite film possesses distinct anisotropic magnetocapacitance effect. When the direction of the magnetic field changes, the magnetocapacitance of the composite film changes from positive value to negative value. Moreover, the magnetocapacitance value changes with the variations of temperature and magnetic field magnitude. Typically, at 300 K a maximum value of positive magnetocapacitance (5.49%) and a minimum value of negative magnetocapacitance of (1.85%) are obtained at -4000 and 4000 kOe, respectively. When the temperature is reduced to 10 K, the positive magnetocapacitance decreases to a minimum value (0.64%) while the negative magnetocapacitance increases to a maximum value (5.4%). We perform a detailed analysis on such a magnetoelectric coupling behavior, and elucidate its origin, which should be attributed to the exchange bias effect and interface-mediated magnetism-stress-electricity coupling process.