We, for the first time, demonstrate a tunable mid-infrared BaGa4Se7-based optical parametric oscillator pumped by a acousto-optical Q-switched Ho:YAG laser at 2090.6 nm. Up to 1.55 W of average power was generated in the 3-5 μm range, corresponding to an optical-to-optical conversion efficiency of 14.4% and a slope efficiency of 19.9%. The mid-IR radiation spectra were also seriously researched at different phase-matched angles. The tunable range was 3.49-4.13 μm for the signal, and 5.19-4.34 μm for the idler.