For the design and management of the modern heavy oil piplines, the application of mathematical model to describe the characteristics of screw pump is crucial to the improvement of design quality and operational management efficiency. According to the features of HOW7T.3(50mm) screw pump’s actual measured data, this research established two groups of mathematical model.The first one described the change of screw pump’s displacement along with the variation of pressure difference and viscosity, while the second group described the change of shaft power along with the variation of pressure difference and viscosity, and then it solved all the four models by a particle swarm optimization (PSO) algorithm. The model-building and model-solving of these two examples showed that the PSO algorithm could rapidly search the best model regression parameter. Through the four target test, the research finally selected two models with relatively high accuracy. In the end, the paper put forward that it is necessary to take further research on the forms of screw pump characteristic mathematical model, and the corresponding optimization method of model-solving, in order to make the models more succinct and with higher fitting precision.