Temporal processing is crucial for auditory perception and cognition, especially for communication sounds. Previous studies have shown that the auditory cortex and the thalamus use temporal and rate representations to encode slowly and rapidly changing time-varying sounds. However, how the primate inferior colliculus (IC) encodes time-varying sounds at the millisecond scale remains unclear. In this study, we investigated the temporal processing by IC neurons in awake marmosets to Gaussian click trains with varying interclick intervals (2-100ms). Strikingly, we found that 28% of IC neurons exhibited rate representation with nonsynchronized responses, which is in sharp contrast to the current view that the IC only uses a temporal representation to encode time-varying signals. Moreover, IC neurons with rate representation exhibited response properties distinct from those with temporal representation. We further demonstrated that reversible inactivation of the primary auditory cortex modulated 17% of the stimulus-synchronized responses and 21% of the nonsynchronized responses of IC neurons, revealing that cortico-colliculus projections play a role, but not a crucial one, in temporal processing in the IC. This study has significantly advanced our understanding of temporal processing in the IC of awake animals and provides new insights into temporal processing from the midbrain to the cortex.