With the improvement of modern radar signal quality and resolution， radar systems can capture more detail on targets. Objects imaged by inverse synthetic aperture radar （ISAR） may have components that rotate at high speeds relative to the whole， such as propeller blades of aircraft. The micro-Doppler effects created by these components may seriously interfere with the imaging results. Therefore， this paper proposes a method to eliminate the micro-Doppler effect in ISAR based on the time recursive iterative adaptive （TRIAA） and compressive sensing. The method uses TRIAA technology to analyze the time-frequency characteristics of signals， removes the micro-Doppler effect from the time-frequency map， and uses the compressive sensing sparse reconstruction technology to accurately restore the effective signal. Experimental results of simulation and measured data verify the effectiveness of the proposed method.