To increase the resolution and signal-to-noise ratio (SNR) of magnetic resonance (MR) images, an adaptively regularized super-resolution reconstruction algorithm was proposed and applied to acquire high resolution MR images from 4 subpixel-shifted low resolution images on the same anatomical slice. The new regularization parameter, which allowed the cost function of the new algorithm to be locally convex within the definition region, was introduced by the piori information to enhance detail restoration of the image with a high frequency. The experiment results proved that the proposed algorithm was superior to other counterparts in achieving the reconstruction of low-resolution MR images.