We propose and demonstrate a broadly wavelength-tunable mode-locked Ho/Pr-codoped ZBLAN fiber laser operating in the 3 μm mid-infrared spectral region based on a semiconductor saturable absorber mirror. Wavelength selection is realized by rotating a plane ruled grating. The fiber laser exhibits stable continuous-wave mode-locking operation over a wide wavelength tuning range of 34 nm (2842.2 nm~2876.2 nm), with a 10.17 MHz repetition rate and 22 ps pulse duration. Stable mode-locked pulses can be maintained until the launched pump power of 1.25 W. Maximum average output power of 127.7 mW and the corresponding pulse energy of 12.56 nJ are achieved. To the best of our knowledge, this is the first demonstration of a wavelength-tunable mode-locked fiber laser operating in the 3 μm spectral region. Such simple, robust, and versatile mid-infrared picosecond laser source can find various applications in laser surgery, spectroscopy, and nonlinear frequency conversion.