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We discuss the possibility of realizing Weyl semimetal phase in themagnetically doped topological band insulators. When the magnetic moments areferromagnetically polarized, we show that there are three phases in the systemupon the competition between topological mass and magnetic mass: topologicalband insulator phase, Weyl semimetal phase, and trivial phase. We explicitlyderive the low energy theory of Weyl points from the general continuumHamiltonian 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 introducethe microscopic tight-binding model on the diamond lattice to describe themagnetically doped topological insulator, and we found the Weyl semimetalphase. We also discuss the dimensional cross-over of the Weyl semimetal phaseto the anomalous Hall effect. In closing, we discuss the experimental situationfor the Weyl semimetal phase.

Possible topological phases of bulk magnetically doped Bi2Se3: turning a topological band insulator into the Weyl semimetal