Motion artifact suppression is an important task in the medical imaging field. Motion during data acquisition can produce blurred images and artifacts. The calculation load for previous motion correction methods is relatively high. In order to decrease computational complexity, an efficient motion correction method is proposed based on fast robust correlation. Fast robust correlation is a computationally efficient search algorithm for translational image matching in the frequency domain. This method calculates the matching surface using a series of high-speed correlations by defining a kernel with sinusoidal terms. The proposed method corrects motion distorted images by aligning translational motion between images formed by neighboring frequency segments. Due to the ineffectiveness of the squared difference kernel to detect motion between partial-Fourier images, the absolute value kernel is proposed, which can be easily approximated by sinusoidal terms. Total variation of the sum of partial-Fourier images is chosen as the new match criterion. FFTs are used to calculate correlations for computational speed. Experimental results show that the proposed method can reduce image motion artifacts effectively and efficiently.