Interferometric inverse synthetic aperture radar (InISAR) is an usually adopted approach for three-dimensional (3D) imaging of noncooperative target with a real or equivalent turntable motion. In practice, the Doppler frequency of non-cooperative target usually vary nonlinearly, especially when the rotational velocity of the target is fast or the imaging time is relatively long, the azimuth echoes of the target often contain quadratic phase terms. In this case, if we do not compensate the nonlinear phase terms contained in the echoes, the ISAR image will be defocused and then the 3D imaging quality will be degraded. Aiming at solving this problem, a new 3D InISAR imaging method based on respective Lv's distribution transformation and iterative Doppler focussing (RLvDT-IDF) is proposed in this paper. The major contributions of the proposed approach are as follows: (1) the echo of a range cell which can be treated as the superposition of a series of linear frequency modulation signals (LFMs) is processed by LvDT to specify the chirp rates (CRs) of these LFMs. The CRs are used to construct phase functions so as to remove the quadratic phase term contained in the echo by the IDF method;(2) Considering that the CRs within a range cell received by different channels are relatively different, so different ISAR images are focussed by respective LvDT-IDF (RLvDT-IDF), so all the well-focussed ISAR images can be obtained, which help to improve the accuracy of the image registration and scatterer extraction; (3) Considering that the phase information from the well-focussed ISAR images may have different errors by the RLvDT-IDF processing and the unfocused ISAR images contain the complete phase information, so they are used instead of the well-focussed ISAR images to estimate the interferometric phases of the extracted scatterers; (4) Based on the estimated CRs and 3D coordinates, the target's 3D rotation vector is retrieved by minimising the sum of squared residuals. Both simulations and practical experiment are conducted to validate the proposed method.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.