In order to clarify the physical mechanism of magnetization step in strong correlation manganites with a phase separation, one Pr5/8Ca3/8MnO3 single crystal was successfully grown by the optical floating-zone method and investigated systematically on its structural, magnetic, and transport properties. One steplike charge ordered antiferromagnetic-ferromagnetic transition was proved below 60 K as an applied magnetic field is only several T, and the step in the M-H curve became ultrasharp below 4.2 K. A history-dependent magnetization effect was also observed. Here, the given charge/orbital ordering and spin structure indicated that the energy difference between ferromagnetic and charge ordering phases was small for Pr5/8Ca3/8MnO3. According to the model of spin and orbital coupling, the steps should be the result of spin reorientation under the magnetic field. Meanwhile, the two sharp step transitions appeared in the different field-cooled(FC) conditions at T=2.0 K, which shows a possible existence of spin quantum transition. The observed history-dependent magnetization reflected the existence of dx2−y2 orbital ordering state within the FM state. The correlation between the magnetic structure and the mechanism was also discussed.