In MRI, motion artifacts can significantly degrade image quality. Motion artifact correction methods using deep neural networks usually required extensive training on large datasets, making them time-consuming and resource-intensive. In this paper, an unsupervised deep learning-based motion artifact correction method for turbo-spin echo MRI is proposed using the deep image prior framework. The proposed approach takes advantage of the high impedance to motion artifacts offered by the neural network parameterization to remove motion artifacts in MR images. The framework consists of parameterization of MR image, automatic spatial transformation, and motion simulation model. The proposed method synthesizes motion-corrupted images from the motion-corrected images generated by the convolutional neural network, where an optimization process minimizes the objective function between the synthesized images and the acquired images. In the simulation study of 280 slices from 14 subjects, the proposed method showed a significant increase in the averaged structural similarity index measure by 0.2737 in individual coil images and by 0.4550 in the root-sum-of-square images. In addition, the ablation study demonstrated the effectiveness of each proposed component in correcting motion artifacts compared to the corrected images produced by the baseline method. The experiments on real motion dataset has shown its clinical potential. The proposed method exhibited significant quantitative and qualitative improvements in correcting rigid and in-plane motion artifacts in MR images acquired using turbo spin-echo sequence.