We demonstrated a widely wavelength-tunable mid-infrared mode-locked Ho3+/Pr3+-codoped ZBLAN fiber laser by using single-wall carbon nanotubes (SWCNTs) with a wide diameter distribution as saturable absorber (SA). This laser emits stable mode-locked pulses in the water vapor transmission window with a maximum average output power of 126.6 mW at a repetition rate of 12.5 MHz. The central wavelength of the mode-locked laser can be continuously tuned from 2836.2 to 2906.2 nm. The 70-nm wavelength tuning range represents the widest tuning range ever achieved in mode-locked Ho3+-doped ZBLAN fiber laser oscillators. Our results also indicate that the SWCNTs can be promising broadband SAs for obtaining gain-bandwidth-limited tunable operation for 3- $\mu \text{m}$ Ho3+-doped ZBLAN fiber lasers. Such simple, reliable, wideband tunable, and low-cost mode-locked mid-infrared fiber laser source is highly attractive for molecular spectroscopy, breath analysis, and laser surgery of human tissue.