We demonstrate continuous-wave laser action in a Yb3+-doped lutetium Yttrium oxyorthosilicate (YbxLuyY1-x-y)2SiO5(YbLYSO) crystal (0.001≤x≤0.5, 0≤y≤0.8). In the free-running operation, we obtained an output power as high as 7.8 W centered about 1086 nm for a 2.5% output coupler, corresponding to a slope efficiency of 64%. Using a SF14 prism as an intracavity tuning element, the tunability of the YbLYSO laser in the spectral range of 1014～1091 nm has been achieved.