Derived-band click-evoked auditory brainstem responses (ABRs) were obtained for normal-hearing (NH) and sensorineurally hearing-impaired (HI) listeners. The latencies extracted from these responses, as a function of derived-band center frequency and click level, served as objective estimates of cochlear response times. For the same listeners, auditory-filter bandwidths at 2 kHz were estimated using a behavioral notched-noise masking paradigm. Generally, shorter derived-band latencies were observed for the HI than for the NH listeners. Only at low click sensation levels, prolonged latencies were obtained for some of the HI listeners. The behavioral auditory-filter bandwidths accounted for the across-listener variability in the ABR latencies: Cochlear response time decreased with increasing filter bandwidth, consistent with linear-system theory. The results link cochlear response time and frequency selectivity in human listeners and offer a window to better understand how hearing impairment affects the spatiotemporal cochlear response pattern.