Defective rotating machinery usually exhibits complex dynamic behavior. Therefore, feature representation of machinery vibration signals is always critical for condition monitoring of rotating machinery. Permutation entropy (PeEn), an adaptive symbolic description, can measure complexities of signals. However, PeEn may lack the capability to fully describe dynamics of complex signals since compressing all the information into a single parameter. Afterwards, multiscale PeEn (MPeEn) is put forward for coping with nonstationarity, outliers and artifacts emerging in complex signals. In MPeEn, a set of parameters serve to describe dynamics of a complex signal in different time scales. Nonetheless, an average procedure in MPeEn may withhold local information of a complex signal. To overcome deficiencies of PeEn and MPeEn, this paper proposes generalized PeEn (GPeEn) by introducing different time lags and orders into PeEn. In GPeEn, a complex signal is compressed into one matrix rather than a single parameter. Moreover, minimal, maximal and average values of a matrix obtained by GPeEn serve to briefly describe conditions of rotating machinery. Next, a numerical experiment proves that GPeEn outperforms PeEn and MPeEn in characterizing conditions of a Lorenz model. Subsequently, the performance of GPeEn is benchmarked against that of PeEn and MPeEn by investigating gear and roll-bearing vibration signals containing different types and severity of faults. The results show that the proposed method has a clear advantage over PeEn and MPeEn in condition monitoring of rotating machinery.