Pressure boundary condition was used to investigate the unsteady 3-D flow characteristics in a single-stage single-suction centrifugal pump with vaneless volute. For the calculation, the total pressure and the static pressure were specified for inlet and outlet respectively, and the sliding mesh technique was used. The results show the capability of this numerical method in capturing the unsteady flow characteristics due to the impeller-volute interaction. The flow is characterized by periodic pulsation, blade passing frequency in volute and impeller rotating frequency in impeller. To a large extent, the asymmetric shape of the volute affects the propagation of impeller-volute interaction and results in the circumferential non-uniformity flow distribution in the pump. 