A diode-end-pumped continuous-wave (CW) and passively Q-switched Ho, Pr:LiLuF4 (Ho, Pr:LLF) laser operation at 2.95 μm was demonstrated for the first time, to the best of our knowledge. The maximum CW output power was 172 mW. By using a monolayer graphene as the saturable absorber, the passively Q-switched operation was realized, in which regimes with the highest output power, the shortest pulse duration, and the maximum repetition rate were determined to be 88 mW, 937.5 ns, and 55.7 kHz, respectively. The laser beam quality factor M2 at the maximum CW output power were measured to be Mx2=1.48 and My2=1.47.