The unsteady response of a turbine exposed to pulsatile incoming flow is studied via the analytical model in this article. First, the response of output torque of the turbine to pulsatile condition is theoretically studied and a correlation of the torque response is deduced. The results confirm that the fluctuations of the torque are proportional to the fluctuations of velocity at the rotor inlet. Next, the unsteady response of turbine system is modeled by the method of transfer matrixes of quasi-2D flow elements connected in sequence. The correlations of swallowing capacity and output torque with the imposed pulsatile inlet pressure are obtained via the models. The results prove that the unsteadiness of turbine performance is proportionally enhanced by the pulse magnitude and the acoustic throttle slope in swallowing capacity curve. In particular, the unsteadiness increases first, but then reduces as the Strouhal number increases. The strongest unsteady performance is achieved when the resonance of the system happens at the Strouhal number as 1. Furthermore, the model proves that the total torque deviation of the turbine is proportional to the mass accumulation in a pulse period. This justifies the validity of the widely used assumption of the mass accumulation as an indicator of turbine performance unsteadiness. Finally, the results of the theoretical model are validated against the 1D gas-dynamic simulation via in-house developed code.