Fault diagnosis of large rotating machinery sets is very important for many industry sectors. However, it is also difficult because of its complexity. The conventional fault diagnosis methods are based on FFT spectral analysis. While its effectiveness has been approved by many applications, it also has significant limitations. In fact, it has been found that many faults have similar spectral patterns. In order to pinpoint the cause of the faults, it may be necessary to vary the speed to get additional information. Nevertheless, the speed variation makes the vibration signal non-stationary. This in turn makes the FFT spectral analysis imperative. In this paper, it is proposed to use a new technique, called evolutionary spectrum, to analyze the non-stationary signal and hence diagnose the faults. First, following a brief introduction of wavelet transform, the evolutionary spectrum is described. Next, the implementation procedure of the evolutionary spectrum is given. Then, by means of computer simulation and experiment results analysis, it is shown that the evolutionary spectrum can effective capture the fault patterns and hence, diagnose rotor unbalance and rotor stiffness asymmetric.