As a fresh way to improve the user viewing experience, videos of time-sync comments have attracted a lot of interest. Many efforts have been made to explore the effectiveness of time-sync comments for various applications. However, due to the complexity of interactions among users, videos, and comments, it still remains challenging to understand users’ behavior on time-sync comments. Along this line, we study the problem of time-sync comment behavior prediction with considerations of both historical behaviors and multi-modal information of visual frames and textual comments. Specifically, we propose a novel Multi-modal short- and long-Range Temporal Convolutional Network model, namely MRT. Firstly, we design two amplified Temporal Convolutional Networks with different sizes of receptive fields, to capture both short- and long-range surrounding contexts for each frame and time-sync comments. Then, we design a bottle-neck fusion module to obtain the multi-modal enhanced representation. Furthermore, we take the user preferences into consideration to generate the personalized multi-model semantic representation at each timestamp. Finally, we utilize the binary cross-entropy loss to optimize MRT on the basis of users’ historical records. Through comparing with representative baselines, we demonstrate the effectiveness of MRT and qualitatively verify the necessity and utility of short- and long-range contextual and multi-modal information through extensive experiments.