To the doubt whether steady flow is endowed with global representativeness, the numerical simulation was performed for a low specific-speed centrifugal pump at multi-phase position, under the designed operating conditions, by multiple reference frame model. Changes of the total head were investigated in detail, due to the relative position of impeller passage to volute. The important flow information, such as velocity, the pressure fields and characteristics of swirling flow and its developing process on the eighth cross-sections of the volute casing, were also gained. It was concluded that the result of steady numerical simulation with multi-phase position truly reflects the unsteady flow features in the pump flow field to a certain degree.