Accurate neural processing of time-varying sound amplitude and spectral information is vital for species-specific communication. During postnatal development, cortical processing of sound frequency undergoes progressive refinement; however, it is not clear whether cortical processing of sound envelope transients also undergoes age-related changes. We determined the dependence of neural response strength and first-spike latency on sound rise–fall time across sound levels in the primary auditory cortex (A1) of juvenile (P20–P30) rats and adult (8–10 weeks) rats. A1 neurons were categorized as “all-pass”, “short-pass”, or “mixed” (“all-pass” at high sound levels to “short-pass” at lower sound levels) based on the normalized response strength vs. rise–fall time functions across sound levels. The proportions of A1 neurons within each of the three categories in juvenile rats were similar to that in adult rats. In general, with increasing rise–fall time, the average response strength decreased and the average first-spike latency increased in A1 neurons of both groups. At a given sound level and rise–fall time, the average normalized neural response strength did not differ significantly between the two age groups. However, the A1 neurons in juvenile rats showed greater absolute response strength, longer first-spike latency compared to those in adult rats. In addition, at a constant sound level, the average first-spike latency of juvenile A1 neurons was more sensitive to changes in rise–fall time. Our results demonstrate the dependence of the responses of rat A1 neurons on sound rise–fall time, and suggest that the response latency exhibit some age-related changes in cortical representation of sound envelope rise time.