In the high-resolution inverse synthetic aperture radar (ISAR) imaging of low-earth-orbit space targets, the received signal from one range bin can be modeled as a multicomponent cubic phase signal (CPS) after motion compensation. The chirp rates and the quadratic chirp rates of the multicomponent CPS need to be estimated with parameter estimation algorithms to obtain the focused ISAR image. In this article, a new parametric range-instantaneous-Doppler ISAR imaging method is proposed, which introduces a new algorithm for parameter estimation of multicomponent CPSs. The cross terms of the generalized cubic phase function (GCPF) are analyzed. By eliminating the cross terms in the ambiguity function domain, the coherent integrated smoothed GCPF (CISGCPF) is proposed to estimate the quadratic chirp rates. Numerical examples are provided to verify the accuracy of the parameter estimation and the effectiveness of the cross-term suppression for CISGCPF in processing multicomponent signals. Simulated and real data imaging results demonstrate the performance of the CISGCPF-based ISAR imaging method. Comparisons with the existing algorithms show that the proposed method is effective in reconstructing focused images with less fake scatterers.