Abstract: Objective To extend the application of Gibbs artifact reduction method that exploits local subvoxel- shifts (LSS) to zero- padded k-space magnetic resonance imaging (MRI) data. Methods We investigated two approaches to extending the application of LSS-based method to under-sampled data. The first approach, namely LSS+ interpolation, utilized the original LSS-based method to minimize the local variation on nonzero-padding reconstructed images, followed by image interpolation to obtain the final images. The second approach, interlaced local variation, used zero-padded Fourier transformation followed by elimination of Gibbs artifacts by minimizing a novel interlaced local variations (iLV) term. We compared the two methods with the original LSS and Hamming window filter algorithms, and verified their feasibility and robustness in phantom and in vivo data. Results The two methods proposed showed better performance than the original LSS and Hamming window filters and effectively eliminated Gibbs artifacts while preserving the image details. Compared to LSS + interpolation method, iLV method better preserved the details of the images. Conclusion The iLV and LSS+interpolation methods proposed herein both extend the application of the original LSS method and can eliminate Gibbs artifacts in zero-filled k-space data reconstruction images, and iLV method shows a more prominent advantage in retaining the image details.