A centrifugal compressor is an important rotating tool that is widely used in the natural gas transportation industry. In engineering practice, working conditions typically deviate from design conditions. For example, inlet pressure and temperature levels are fixed in design conditions, whereas these two parameters are unstable under actual working conditions. Moreover, the physical properties of actual gas are often different from those of designed gas. As a result, it is difficult for a design performance curve to accurately predict the actual performance of a compressor. Therefore, it is necessary to study compressor performance conversions based on similarity criteria. At present, three primary methods are used for the conversion of compressor performance, i.e., the complete similarity conversion method, the first similarity conversion method and the second similarity conversion method. The complete similarity method adheres to very strict requirements, and it is difficult to completely meet such requirements in practical engineering settings. The first similarity conversion method is based on an assumption of polytrophic processes, and it is suitable to apply to gases with different adiabatic index values. For this method, temperature conversion results are accurate, but pressure conversion results are less accurate. The second similarity conversion method is based on an assumption of isometric processes. In contrast to the first similarity conversion method, the pressure conversion results of this method are accurate, but the temperature conversion results are less accurate. This is attributed to different means of determining the pressure ratio according to similarity conversion methods. If calculations of pressure ratios could apply the advantages and overcome the disadvantages of the first and second similarity conversion methods, the accuracy of performance conversion methods could be effectively improved. Based on the above, a new similarity conversion method for centrifugal compressors based on the predictor-corrector method is proposed. According to the proposed method, the second similarity conversion method is first used to predict the pressure ratio, and the first similarity conversion method is subsequently used to correct the pressure ratio. Thus, the pressure ratio can be corrected to ensure that both pressure and temperature conversion results are accurate. Finally, the first and second similarity conversion methods and the proposed method are used to convert the performance curve of a compressor used in the natural gas transmission pipeline running from Sichuan to eastern China. Compared with the field test data, the conversion errors of these three methods are as follows: for the first similarity conversion method, the relative of the outlet pressure is about 6% and the error of the outlet temperature is about 4–7°C; for the second similarity conversion method, the relative of the outlet pressure is about 4% and the error of the outlet temperature is about 2°C; for the proposed method, the relative of the outlet pressure is about 2% and the error of the outlet temperature is about 2°C. The results show that the method proposed in this paper is significantly more accurate than the other two common methods. Therefore, the use of this new method for compressor performance conversion in actual engineering settings is recommended.