The invention relates to a construction method of a full-characteristic mathematical model of a mixed-flow pump. Aiming at the mixed-flow pump, the invention discloses the mathematical model meeting research and engineering requirements; after accurate values of all coefficients included in the mathematical model are calculated through test data, the mathematical model with all known coefficients can be obtained and is used for describing an external characteristic of the mixed-flow pump under all conditions of full characteristics. The mathematical model provided by the invention is high in precision and high in correlation with the full characteristics of the mixed-flow pump, and can be well fitted with the test data and also accurately forecast the external characteristic of a working condition point without the test data. The mathematical model provided by the invention supplies an important mathematical basis to the research on the full characteristics of the mixed-flow pump by using a mathematical method.