Abstract At present, tested pump performance data are usually fitted with a single polynomial. This method suffers from several disadvantages, such as poor accuracy in irregular or saddle-shaped performance curve fitting, unfavourable approximation to the actual data or even deviation from the actual experimental characteristic data and so on. By comparing various curve fitting methods for pump performance data, the advantages and disadvantages of these methods are analyzed, and a piecewise least squares polynomial curve fitting method is designed for special saddle-shaped pump performance data. To make sure the continuity and differentiability of piecewise fitted curves, a differential fitting method was adopted to connect the boundary points between two piecewise curves. Finally, a set of experimental pump performance data is fitted by using piecewise least square 3rd-order polynomials and a 5th-order single polynomial, respectively, and the fitted results are analyzed. It is shown that the piecewise least squares 3rd-order polynomial curve fitting method can improve the accuracy in complex performance curve fitting, as a result, the continuity between two fitted curves is guaranteed.