A new fault recognition method for centrifugal compressor was proposed by using entropy weight-based gray relational analysis (EW-GRA). Firstly, the weight values of all fault features were calculated objectively by the entropy method to avoid the influence of subjective factors. Secondly, an improved local gray relational coefficient (LGRC) formula with weight measures was designed to reflect the contributions of different fault features. Thirdly, according to the relationship between similarity degree and Euclidean distance, the local gray relational distances (LGRD), the global gray relational distances (GGRD) and the global gray relational grades (GGRG) were calculated, and consequently, the fault recognition result was obtained by using the max membership degree principle. Finally, the engineering practicability and validity of the EW-GRA method was demonstrated by a centrifugal compressor fault diagnosis example, and the results show that the EW-GRA method is more effective and accurate than the traditional gray relational analysis (T-GRA) method and the weighted gray relational analysis (W-GRA) method.