The compressor is operated at unsteady exit conditions in many scenarios such as the instability of combustion in gas turbine and denotation engine. The aerodynamic stability of the compressor is inevitably influenced by the unsteady operating environment. In this paper, a one-dimensional (1D) model that combines pulsation and unsteady responses of the compressor is developed to investigate the stability of the compressor system. The results show that the onset of surge and the transient responses of the compressor during surge are well predicted by the method. The amplitude of the component at surge frequency obtained by fast Fourier transformation (FFT) method is applied as a criterion to quantitively evaluate the onset and the strength of the surge. Compressor stability is enhanced at pulsating conditions due to the interaction between forced oscillation of pulsation and self-sustained oscillation of surge. An analytical model is established to understand the mechanism of the enhancement of compressor stability under pulsation. The change of total energy of the compressing system is proposed to evaluate the influence of pulsating conditions. Specifically, the energy change is reduced for pulsation conditions due to two aspects: the lower slope of compressor characteristic curve due to the lag-effect of compressor responses and the higher energy dissipation due to the nonlinear throttling effect.