Overdoped Bi 2Sr 2CaCu 2O 8+ δ (Bi-2212) single crystals have been prepared by travelling solvent floating zone technique under high oxygen pressure up to 10 bar. The effect of oxygen pressure on growth conditions is studied. In contrast with air growth the instability of molten zone occurs under high oxygen pressure applied during the growth, in consequence of the precipitation of impurity phases on crystallization front. The feed rods pre-melted over 4 bar oxygen pressure were found to contain minor impurity phases, and this could also affect the stability of molten zone. With increasing oxygen pressure from 2 to 10 bar the ratio of Bi/Sr for the overdoped Bi-2212 crystals increases in subsequent to the decrease of c-axis from 30.890(6) to 30.653(8) Å, while the Tc reduces from 95 to 81 K. Besides the oxygen growth pressure Tc and ∆Tc of the overdoped crystals are influenced by growth rate and feed rod pre-melting conditions.