The impeller of a single-blade centrifugal pump has an asymmetric characteristic, and the secondary flow vortex is easy to form in the spiral volute, which will induce high pressure fluctuation and affect the safety and stability of the pump system. In order to reveal the unsteady characteristics of the secondary flow inside the spiral volute, a single-blade centrifugal pump was chosen as the research object to investigate by numerical simulation. The SST k-ω model was applied to simulate the three-dimensional unsteady viscous incompressible flow in the centrifugal pump. The predictions of the numerical model were compared with experimental results, and it showed good agreement between the simulation and experiment results. The pressure fluctuation characteristics of single-blade centrifugal pump under multiple conditions were studied. The results showed that the flow field in the pump presented obvious pressure fluctuation characteristics under different flow conditions. The pressure fluctuation intensity of the first section of the volute was the lowest, and the pressure fluctuation intensity of the second section was the highest. The dominant frequency of pressure fluctuations was the blade pass frequency. With the increase of the flow rate, the amplitude of the dominant frequency was decreased. Then the secondary flow inside the spiral volute of the single-blade centrifugal pump was further analyzed. Under the three flow rate conditions, the secondary flow vortex appeared in the volute, the shape of which showed obvious periodicity. The magnitude of cross flow velocity was decreased firstly and then increased with the increase of the flow rate. It was relatively small under the design flow condition while it was increased significantly under off-design condition. The research can provide theoretical basis for the safe and stable operation of single-blade centrifugal pumps.