Real-time transient stability assessment (TSA) is an important task which ensures the stability, and therefore, enhances the reliability of power systems. Various types of learning-based methodologies in which machine learning and deep learning algorithms are adopted for real-time TSA exist in literature. Convolutional neural network (CNN) is a deep-learning-based method which mostly demonstrates high performance for image classification. However, employing the conventional structure of CNN classifier for time series data may result in high computational complexity or low prediction accuracy. In this paper, a novel methodology is proposed for real-time stability prediction of a power system in which voltage angle measurements obtained from PMUs are utilized to train a multichannel deep CNN (MC-DCNN), which is a modified version of CNN classifier and appropriate for multivariate time series data. To evaluate the performance of the proposed method for real-time transient stability prediction, it is applied to the 127-bus WSCC test system.