We have measured the field-cooled (fc) and zero-field-cooled (zfc) magnetizations of 110°C annealed La2CuO4+δ for 0 <δ< 0.12. We found that the Meissner signals (fc magnetizations) and shielding signals (zfc magnetizations) are almost right on top of each other except at very low temperatures close to 5 K. In particular, at 6 = 0.03, an anomalously large irreversible magnetization at low temperatures and unusual paramagnetic signals are observed at Tc. We suggest that the observed anomalies are intrinsic and are electronic in origin which is closely related to the existence of a critical hole concentration at Pc ≅ 0.06.