  We discuss the possibility of realizing Weyl semimetal phase in the
magnetically doped topological band insulators. When the magnetic moments are
ferromagnetically polarized, we show that there are three phases in the system
upon the competition between topological mass and magnetic mass: topological
band insulator phase, Weyl semimetal phase, and trivial phase. We explicitly
derive the low energy theory of Weyl points from the general continuum
Hamiltonian of topological insulators near the Dirac point, e.g. ${\bf k} \cdot
{\bf p}$ theory near $\Gamma$ point for Bi_{2}Se_{3}. Furthermore, we introduce
the microscopic tight-binding model on the diamond lattice to describe the
magnetically doped topological insulator, and we found the Weyl semimetal
phase. We also discuss the dimensional cross-over of the Weyl semimetal phase
to the anomalous Hall effect. In closing, we discuss the experimental situation
for the Weyl semimetal phase.
