In this paper, we propose a novel technique for skull stripping of infant (neonatal) brain magnetic resonance images using prior shape information within a graph cut framework. Skull stripping plays an important role in brain image analysis and is a major challenge for neonatal brain images. Popular methods like the brain surface extractor (BSE) and brain extraction tool (BET) do not produce satisfactory results for neonatal images due to poor tissue contrast, weak boundaries between brain and non-brain regions, and low spatial resolution. Inclusion of prior shape information helps in accurate identification of brain and non-brain tissues. Prior shape information is obtained from a set of labeled training images. The probability of a pixel belonging to the brain is obtained from the prior shape mask and included in the penalty term of the cost function. An extra smoothness term is based on gradient information that helps identify the weak boundaries between the brain and non-brain region. Experimental results on real neonatal brain images show that compared to BET, BSE, and other methods, our method achieves superior segmentation performance for neonatal brain images and comparable performance for adult brain images.