Neonatal magnetic resonance (MR) images typically have low spatial resolution and insufficient tissue contrast. Interpolation methods are commonly used to upsample the images for the subsequent analysis. However, the resulting images are often blurry and susceptible to partial volume effects. In this paper, we propose a novel longitudinally guided super-resolution (SR) algorithm for neonatal images. This is motivated by the fact that anatomical structures evolve slowly and smoothly as the brain develops after birth. We propose a strategy involving longitudinal regularization, similar to bilateral filtering, in combination with low-rank and total variation constraints to solve the ill-posed inverse problem associated with image SR. Experimental results on neonatal MR images demonstrate that the proposed algorithm recovers clear structural details and outperforms state-of-the-art methods both qualitatively and quantitatively.