A series of oxygen-doped RE2CuO4 (RE=Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm) was synthesized using high-pressure/oxygen-doped technique. The structures and low temperature magnetic properties were investigated. The XRD patterns indicate that the structures of high oxygen pressure RE2CuO4 (only for RE=Sm, Eu) samples are pure T phase, but when RE= Gd, Tb, Dy, Ho, Er, Tm, the structures turn to disorder. The magnetic anomalies that occurred at T～30 K are observed in high oxygen pressure RE2CuO4. It is found that the transition temperatures of weak ferromagnetic anomalies are nearly independent of the rare-earth components. Thus, the O-doping plays an important role in anomalous magnetic properties of RE2CuO4+δ. The magnetic anomalies in RE2CuO4 are considered to be due to ferromagnetic clusters formed in the Cu-O plane after the oxygen doping.