New Yb-doped crystal Yb3+∶Lu2SiO5 (Yb∶LSO) lasers pumped by diode-laser at 976 nm with passively Q-switched and multi-wavelength continuous-wave (CW) output were demonstrated. The maximum CW output power was 490 mW with the absorbed pump power of 2.57 W. The slope efficiency and optical-optical conversion efficiency were 22.2% and 14.2% respectively. The threshold was 299 mW, and the laser wavelength was 1084 nm. The wavelength could be tunable from 1034 to1085 nm with a prism. For the Q-switched output, the laser operated at 1058 nm with an InGaAs semiconductor saturable absorber mirror (SESAM). The Q-switched output slope efficiency of 3.0% with the maximum absorbed pump power of 1.73 W was also obtained. The pulse repetition rate was 25～39 kHz and was increased with the pump power increased.