The formation and evolution characteristics of bcc phase during the isothermal relaxation processes for supercooled-liquid and amorphous Pb were investigated by molecular dynamics simulation and cluster-type index method (CTIM). It is found that during the relaxation process, the formation and evolution of bcc phase are closely dependent on the initial temperature and structure. During the simulation time scale, when the initial temperature is in the range of supercooled liquid region, the bcc phase can be formed and kept a long time; while it is in the range of glassy region, the bcc phase can be formed at first and then partially transformed into hcp phase; when it decreases to the lower one, the hcp and fcc phases can be directly transformed from the glassy structure without undergoing the metastable bcc phase. The Ostwald's "step rule" is impactful during the isothermal relaxation process of the supercooled and glassy Pb, and the metastable bcc phase plays an important role in the precursor of crystallization.