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This paper develops a hierarchical deep learning machine (HDLM) to efficiently achieve both quantitative and qualitative online transient stability prediction (TSP). For the sake of improving its online efficiency, multiple generators’ fault-on trajectories as well as the two closest data-points in pre-/post-fault stages are acquired by PMUs to form its raw inputs. An anti-noise graphical transient characterization technique is tactfully designed to transform multiplex trajectories into 2-D images, within which system-wide transients are concisely described. Then, following the divide-and-conquer philosophy, the HDLM trains a two-level convolutional neural network (CNN) based regression model. With stability margin regressions hierarchically refined, it manages to perform reliable and adaptive online TSP almost immediately after fault clearance. Test results on the IEEE 39-bus test system and the real-world Guangdong Power Grid in South China demonstrate the HDLM's superior performances on both stability status and stability margin predictions. [ABSTRACT FROM AUTHOR]