In the case of a stepped-frequency waveform (SFW) inverse synthetic aperture radar (ISAR) system, the translational motion (TM) of a target can be usually divided into two parts: 1) target motion within a pulse repetition interval, called the inter-pulse translational motion (IPTM) and 2) target motion between bursts, called the inter-burst translational motion (IBTM). The former induces severe blurring in the ISAR images as well as range-compressed data (i.e., range profile), and the latter also causes dramatic degradation of the ISAR image quality. In this paper, a novel framework for high-resolution gapped SFW (GSFW) ISAR imaging of high-speed maneuvering target is proposed. The main novelty of the proposed method is twofold: 1) accurate TM parameter estimation in conjunction with a compressive sensing theory using a newly devised cost function and particle swarm optimization and 2) compensation for both the IPTM and IBTM phase errors simultaneously even with the GSFW data set. Simulation results using ideal point scatterers show that the proposed method is capable of precise reconstruction of ISAR image and accurate TM parameter estimation. Experimental results using real measured data verify the robustness and the effectiveness of the proposed method.