Computational fluid dynamics were used to study the three-dimensional unsteady flows in a closed pipeline system with a screw-type centrifugal pump during rapid starting period. The unsteady Reynold time-averaged Navier-Stokes equations, RNG have been used to solve the unsteady, incompressible, viscous turbulent effects. The sliding mesh technique is proposed to resolve the transient flows caused by the started impeller. Combined with the characteristics of the motor, the screw-type centrifugal pump was started by two different way of linear and exponential acceleration. The automatic update of the rotational speed variation of field around the impeller was realized by FLUENT UDF. The transient variation of the pressure at the pump inlet and outlet, the global performance characteristics and the transient flow evolutions were obtained under different start-up modes. The results show that the rapid starting period presents obvious transient effect; the transient head, power curves changing with time reveal the transient attachment head and additional power part. Compared with the linear mode, the transient flow, shaft power, efficiency tend to a steady state value within a relatively short period in setting start time and maintain a quasi-periodic fluctuations.