We present a novel model for timing behavior. This model is based on the firing property of neurons in the superficial layers of the posterior cingulate granular retrosplenial cortex (GRS) and does not require a unit-time clock. Suppose that event B occurs N seconds after event A and triggers behavior C. By our behavioral, physiological and anatomical experiments, we found the following facts. 1) Thalamic input carrying sensory information, A, is provided to the superficial layers of the GRS and delayed by the lateral cascading connection within the layers. 2) Hippocampal input (recall information, B) is provided to the deep layers of the GRS. 3) The GRS neurons show timing behavior that is dependent on the trial cycle. 4) Lesioning the GRS impaired the acquisition of trace fear memory and the production of fear-induced freezing behavior, C. Thus we would propose that neural circuits in the GRS play a crucial role in the animal behaviors requiring time discrimination. The question of whether Hebbian learning occurs at the convergent neurons that integrates thalamic and hippocampal information remains unanswered.