Manipulation of the valley degree of freedom provides a new path for quantum information technology, but the real intrinsic large valley-polarization materials are few reported up to date. Here, we perform first-principles calculations to predict a class of 2H-phase single layer (SL) materials LuX
2 (X=Cl, Br, I) to be ideal candidates. SL-LuX
2 are ferrovalley materials with a giant valley-polarization of 55~148 meV as a result of its large spin-orbital coupling (SOC) and intrinsic ferromagnetism (FM). The magnetic transition temperatures of SL-LuI2 and SL-LuCl2 are estimated to be 89~124K, with a sizable magnetic anisotropy with out-of-plane direction. Remarkably, the anomalous valley Hall effect (AVHE) can be controlled in SL-LuX
2 when an external electric field is applied. Moreover, the intrinsic valley-polarization of SL-LuI2 is highly robust for biaxial strain. These findings provide a promising ferrovalley material system for the experiment of valleytronics and the subsequent application.