  The valley-polarized quantum anomalous Hall effect (VQAHE) attracts intensive
interest since it uniquely combines valleytronics and spintronics with
nontrivial band topology. Here, based on first-principles calculations and
Wannier-function-based tight-binding (WFTB) model, we reveal that valley-based
Hall effects and especially the VQAHE induced by external magnetic fields can
occur in two-dimensional (2D) ferromagnetic van der Waals heterostructures
(vdWHs). The results show that considerable valley-splitting derived from the
Zeeman exchange energy drives these vdWHs generating the valley anomalous Hall
effect and then the VQAHE. The chiral edge states and quantized Hall
conductance are utilized to confirm the presence of VQAHE. Besides, it is also
found that external electric fields (or tuning interlayer distances) can
facilitate the realization of VQAHE, and thus we present a phase diagram in a
broad parameter regime of magnetic fields and electric fields (or interlayer
distances). Our work not only offers a class of ferromagnetic vdWHs to realize
various valley-based Hall phases, but also can guide advancements for designing
topological devices with spin-valley filtering effects based on the VQAHE.
