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Objective In order to improve the reconstruction effect of MR images and reduce the noise of reconstructed images, this paper proposes an MRI fast iterative shrinkage thresholding algorithm (FISTA) based on curvelet transform.Methods using the characteristics of curvelet transform as multi-scale, anisotropy, better geometrical expression of image edges, we combine the curvelet sparse transform with FISTA, and compare the same MR image with the traditional FISTA.The quality of the reconstructed image is measured by peak signal to noise ratio (PSNR) , mean square error (MSE) , and structural similarity degree (SSIM) .Results Lena image and brain MR image are used in the experiment.The reconstruction effect of the algorithm is compared and analyzed from the three aspects as the details of reconstruction image, the difference image and the evaluation parameter.The curvelet-FISTA algorithm can effectively recover the undersampled data of the completely sampled image from the magnetic resonance imaging.Conclusions Compared with the traditional FISTA based on the wavelet transform, this method can better maintain the detailed information of the reconstructed image and effectively eliminate blurring at the edges of the image and shows a good reconstruction effect.