We have demonstrated the continuous wave and passively Q-switched Tm, Mg: LiTaO3 lasers for the first time. In continuous wave (CW) regime, a maximum CW output power of 1.03 W at 1952 nm was obtained, giving a slope efficiency of 9.5% and a beam quality M2 = 2.2. In passive Q-switching regime, a single walled carbon nanotube (SWCNT) was employed as saturable absorber (SA). The Tm,Mg:LiTaO3 laser has yielded a pulse of 560 ns under repetition rate of 34.2 kHz at 1926 nm, corresponding to a single pulse energy of 10.1 μJ. The results indicate a promising potential of nonlinear crystals in the applications for laser host materials.