Facial expression recognition (FER) is a challenging problem in the fields of pattern recognition and computer vision. The recent success of convolutional neural networks (CNNs) in object detection and object segmentation tasks has shown promise in building an automatic deep CNN-based FER model. However, in real-world scenarios, performance degrades dramatically owing to the great diversity of factors unrelated to facial expressions, and due to a lack of training data and an intrinsic imbalance in the existing facial emotion datasets. To tackle these problems, this paper not only applies deep transfer learning techniques, but also proposes a novel loss function called weighted-cluster loss, which is used during the fine-tuning phase. Specifically, the weighted-cluster loss function simultaneously improves the intra-class compactness and the inter-class separability by learning a class center for each emotion class. It also takes the imbalance in a facial expression dataset into account by giving each emotion class a weight based on its proportion of the total number of images. In addition, a recent, successful deep CNN architecture, pre-trained in the task of face identification with the VGGFace2 database from the Visual Geometry Group at Oxford University, is employed and fine-tuned using the proposed loss function to recognize eight basic facial emotions from the AffectNet database of facial expression, valence, and arousal computing in the wild. Experiments on an AffectNet real-world facial dataset demonstrate that our method outperforms the baseline CNN models that use either weighted-softmax loss or center loss.