We present the results of electrical resistivity, ac specific heat, magnetic susceptibility, x-ray absorption spectroscopy (XAS), and x-ray magnetic circular dichroism (XMCD) of the ternary iron arsenide EuFe2As2 single crystal under pressure. Applying pressure leads to a continuous suppression of the antiferromagnetism associated with Fe moments and the antiferromagnetic transition temperature becomes zero in the vicinity of a critical pressure P-c similar to 2.5-2.7 GPa. Pressure-induced reentrant superconductivity, which is highly sensitive to the homogeneity of the pressure, only appears in the narrow pressure region in the vicinity of P-c due to the competition between superconductivity and the antiferromagnetic ordering of Eu2+ moments. The antiferromagnetic state of Eu2+ moments changes to the ferromagnetic state above 6 GPa. We also found that the ferromagnetic order is suppressed with further increasing pressure, which is connected with a valence change of Eu ions.