After pointing out the possible problems with the traditional typology of “the Moving Time Metaphor” and “the Moving Ego Metaphor”, this study proposes a new cognitive framework for the spatialized temporal metaphor, i.e. “Time-moving-dependent Metaphor” and “Ego-moving-dependent Metaphor” on the basis of the metonymy of “Event-for-Time”. This framework can be used to account for the metaphorical mapping of time from the space domain. It is revealed that in natural languages what the temporal front-back relation represents is the spatial front-back relation of the different events in the primary reference frame, and that the motion directions of the events and the spatial front-back relation are dependent on the choice of the reference entity in the secondary reference frame. Such an account enhances our understanding for the concept of time in that it reduces the previous different metaphor models to the choice of the reference entity in the secondary reference frame.