We experimentally demonstrated a compact single-wall carbon-nanotube (SWNT)-based deep-red passively Q-switched Pr3+-doped ZBLAN all-fiber laser operating at 716 nm. A free-standing SWNT/polyvinyl alcohol composite film embedded between a pair of fiber connectors was employed as a saturable absorber (SA). The deep-red Q-switched operation is attributed to the combination of implementing a pair of fiber end-facet mirrors to achieve the linear laser resonator and incorporating a SWNT-SA into the cavity as a Q-switcher. Stable short-pulse generation with a duration of 2.3 μs was realized. When gradually increasing the incident pump power, the pulse repetition rate can be linearly tuned from 32.6 to 86.5 kHz, corresponding to a maximum average output power of 1.5 mW and the highest single-pulse energy of 18.3 nJ. To the best of our knowledge, this is the first demonstration of SWNT-based SA for a Q-switched laser at a deep-red wavelength ∼716 nm.