Ferrovalley materials can achieve manipulation of the valley degree of freedom with intrinsic spontaneous valley polarization introduced by their intrinsic ferromagnetism. A good ferrovalley material should possess perpendicular magnetic anisotropy (PMA), valence band maximum (VBM)/conduction band minimum (CBM) at valley points, strong ferromagnetic (FM) coupling and proper valley splitting. In this work, the monolayer GdCl2 is proposed as a potential candidate material for valleytronic applications by the first-principles calculations. It is proved that monolayer GdCl2 is a FM semiconductor with the easy axis along out of plane direction and strong FM coupling. A spontaneous valley polarization with a valley splitting of 42.3 meV is produced due to its intrinsic ferromagnetism and spin orbital coupling (SOC). Although the VBM of unstrained monolayer GdCl2 is away from valley points, a very small compressive strain (about 1%) can make VBM move to valley points. We propose a possible way to realize anomalous valley Hall effect in monolayer GdCl2 by piezoelectric effect, not an external electric field, namely piezoelectric anomalous valley Hall effect (PAVHE). This phenomenon could be classified as piezo-valleytronics, being similar to piezotronics and piezophototronics. The only independent piezoelectric strain coefficient d11 is -2.708 pm/V, which is comparable to one of classical bulk piezoelectric material α-quartz (d11=2.3 pm/V). The biaxial in-plane strain and electronic correlation effects are considered to confirm the reliability of our results. Finally, the monolayer GdF2 is predicted to be a ferrovalley material with dynamic and mechanical stabilities, PMA, VBM at valley points, strong FM coupling, valley splitting of 47.6 meV, and d11 of 0.584 pm/V. Our works provide a possible way to achieve anomalous valley Hall effect by piezoelectric effect, which may stimulate further experimental works related with valleytronics.