We report on the first continuous-wave mid-infrared Tm:Y3Al5O12 laser operating on the 3H4 → 3H5 transition. The 3.2 at.% Tm:Y3Al5O12 laser generated a maximum output power of 1.07 W at ~2.19 & 2.32 μm with a high slope efficiency of 46.3% (vs. the absorbed pump power) exceeding the Stokes limit. Depending on the output coupling and the pump power, a set of discrete laser lines in the range of 2.164–2.346 μm was observed. The spectroscopic properties of Tm:Y3Al5O12 relevant for the mid-infrared laser operation are revised. The maximum stimulated-emission cross-section for the 3H4 → 3H5 transition is 0.35 × 10−20 cm2 at 2324 nm and the emission bandwidth is ~37 nm. The overlap of the 3F4 → 3H6 and the 3H4 → 3H5 transitions is quantified revealing the formulas for Stokes and anti-Stokes phonon sidebands of emission bands. Tm:Y3Al5O12 is promising for broadly tunable (2.1–2.5 μm) and mode-locked mid-infrared oscillators.