Facial expressions are considered a reliable indicator in neonatal pain assessment. This paper proposes a new neonatal pain expression recognition method, which utilizes the feature descriptors based on weighted Local Binary Pattern (LBP) and the classifier based on sparse representation. Firstly, the normalized facial image is described using a feature vector, which is histogram sequence obtained by concatenating the weighted histograms of the LBP maps of all the local blocks. Then, the Principal Component Analysis (PCA) method is used to reduce the dimension of the feature vector. Finally, the classifier based on sparse representation is applied to classify test sample into four classes of facial expressions: calm, crying, moderate pain, severe pain. The objective of this study is to assist the clinicians in assessing neonatal pain by utilizing computer-based image analysis techniques. The experimental results on neonate facial image database show the effectiveness of the proposed algorithm. The classification accuracy is up to 85.50%.