In this article, we introduce a new neonatal facial expression database for pain analysis. This database, called facial expression of neonatal pain (FENP), contains 11,000 neonatal facial expression images associated with 106 Chinese neonates from two children's hospitals, i.e., the Children's Hospital Affiliated to Nanjing Medical University and Second Affiliated Hospital Affiliated to Nanjing Medical University in China. The facial expression images cover four categories of facial expressions, i.e., severe pain expression, mild pain expression, crying expression and calmness expression, where each category contains 2750 neonatal facial expression images. Based on this database, we also investigate the pain facial expression recognition problem using several state-of-the-art facial expression features and expression recognition methods, such as Gabor+SVM, LBP+SVM, HOG+SVM, LBP+HOG+SVM, and several Convolutional Neural Network (CNN) methods (including AlexNet, VGGNet, GoogLeNet, ResNet and DenseNet). The experimental results indicate that the proposed neonatal pain facial expression database is very suitable for the study of both neonatal pain and facial expression recognition. Moreover, the FENP database is publicly available after signing a license agreement (the users can contact Jingjie Yan (yanjingjie@njupt.edu.cn), Guanming Lu (lugm@njupt.edu.cn)) or Xiaonan Li (xnli@njmu.edu.cn).