[Objectives] To clarify the characteristics of unsteady force spectrum of a pump-jet running under inflow turbulent, [Methods] the turbulence grid and Fourier synthesis method is employed to produce incoming turbulence with spatial flow structure and temporal fluctuation, which is combined with LES (large eddy simulation) to obtain broadband unsteady force spectrum of the pump-jet. [Results] The results show that the proposed method could obtain the unsteady force broadband spectrum for duct, stator and rotor. The unsteady force broadband spectrum of the pump-jet is composed of the "hump" around the blade passing frequency and its multiples, the characteristic line spectrum at the stator blade passing frequency and shaft frequency of adjacent stator multiples. With the number of blades increasing, the "hump" becomes more obvious, the characteristic peak changes periodically and reaches the minimum when the number of blades is the number of rotors. Due to the use of the stator and duct, the amplitude of the unsteady force broadband spectrum of the pump-jet is higher than propeller, but the "hump" is not as obvious as propeller. [Conclusions] The research is helpful to clarify the unsteady force characteristics of pump-jet induced by turbulence, and provide ideas for the vibration and noise reduction of pump-jet.