Source camera identification is a fundamental area in forensic science, which deals with attributing a photo to the camera device that has captured it. It provides useful information for further forensic analysis, and also in the verification of evidential images involving child pornography cases. Source camera identification is a difficult task, especially in cases involving small-sized query images. Recently, many deep learning-based methods have been developed for camera identification, by learning the camera processing pipeline directly from the images of the camera under consideration. However, most of the proposed methods have considerably good identification accuracy for identifying the camera models, but less accurate results on individual or instance-based source camera identification. In this paper, we propose to train an accurate deep residual convolutional neural network (ResNet), with the use of curriculum learning (CL) and preprocessed noise residues of camera images, so as to suppress contamination of camera fingerprints and extract highly discriminative features for camera identification. The proposed ResNet consists of five convolutional layers and two fully connected layers with residual connections. For the curriculum learning in this paper, we propose a manual and an automatic curriculum learning algorithm. Furthermore, after training the proposed ResNet with CL, the flattened output of the last convolutional layer is extracted to form the deep features, which are then used to learn one-vs-rest linear support vector machines for predicting the camera classes. Experimental results on 10 cameras from the Dresden database show the efficiency and accuracy of the proposed methods, when compared with some existing state-of-the-art methods.