Atmospheric pressure dielectric barrier discharge (DBD) has attracted widespread attention due to its broad applications in plasma processing, environmental remediation, and biomedical fields. Existing research primarily focuses on the discharge mechanism and parameter effects in plate or needle-plate configurations, while systematic studies on coaxial structures remain relatively scarce. In this study, a fluid model is employed to investigate the discharge process of atmospheric-pressure humid air DBD in a coaxial configuration under nanosecond pulsed voltage excitation. The results indicate that within one cycle, the rising and falling edges of the nanosecond pulsed voltage generate two current pulses of unequal magnitude. The discharge process initiates as Townsend discharge, rapidly transitions to glow discharge during the current pulse, and decays back to Townsend discharge after the pulse ends. Furthermore, as the applied voltage amplitude increases, the peak gap current rises accordingly. Shorter pulse rise/fall times lead to earlier discharge initiation and higher current density.