Personalized image caption, a natural extension of the standard image caption task, requires to generate brief image descriptions tailored for users' writing style and traits, and is more practical to meet users' real demands. Only a few recent studies shed light on this crucial task and learn static user representations to capture their long-term literal-preference. However, it is insufficient to achieve satisfactory performance due to the intrinsic existence of not only long-term user literal-preference, but also short-term literal-preference which is associated with users' recent states. To bridge this gap, we develop a novel multimodal hierarchical transformer network (MHTN) for personalized image caption in this paper. It learns short-term user literal-preference based on users' recent captions through a short-term user encoder at the low level. And at the high level, the multimodal encoder integrates target image representations with short-term literal-preference, as well as long-term literal-preference learned from user IDs. These two encoders enjoy the advantages of the powerful transformer networks. Extensive experiments on two real datasets show the effectiveness of considering two types of user literal-preference simultaneously and better performance over the state-of-the-art models.