Centrifugal pump is an important kind of water injection equipment used to maintain reservoir pressure in oilfield development. The health condition evaluation of centrifugal pumps is helpful to improve the operation and maintenance level. Although Analytic Hierarchy Process (AHP) and fuzzy evaluation method are widely applied in health condition assessment, there are still some problems, such as the determination of weight is greatly influenced by subjective factors and the calculation is complicated. To solve the above problems, this paper puts forward a catastrophe theory evaluation model combining fuzzy mathematics for the evaluation of centrifugal pump. Firstly, the structure, common faults model and operation mechanism of centrifugal pump units were considered, a multi-level security evaluation index system was established; combined with fuzzy mathematics, the bottom indexes used to evaluate centrifugal pump unit was calculated by dimensionless method; and various indicators of the impact of centrifugal pump operation have been processed with standardization and normalization. Secondly, the total security membership value layer by layer was obtained by using the security membership value of the underlying index layer, recursive quantization. Finally, the health level of the centrifugal pump unit was obtained according to the scores obtained by the catastrophe progression. The method takes the advantage of avoiding the quantification of assessing indexes and the choice of parameter values. Thus, the results of this evaluation model are reliable, and the evaluation method is objective, accurate and has a high value in engineering.