During magnetospheric substorms, magnetic reconnection occurs in the near tail and causes the formation of plasmoids. In this paper, we present Geotail observations of periodic magnetic reconnection and plasmoids in the near tail. On April 17--18, 2002, Geotail was located in the northern lobe and detected ten cycles of magnetic field compressions within 24 hours, and southward turnings of the magnetic field Bz component or formations of plasmoids were clearly identified in the first seven cycles. The average period of the plasmoids was ~2.5 hours. A solar wind pressure impulse appeared to trigger the first magnetic compression (or plasmoid). Plasmoids continued to occur for many cycles after the solar wind pressure and interplanetary magnetic field had become stable. The observations suggest that substorms can be periodic and that the periodic substorms can occur without requirement of continuous external triggering.