  We consider complex surfaces, viewed as smooth $4$-dimensional manifolds,
that admit hyperelliptic Lefschetz fibrations over the $2$-sphere. In this
paper, we show that the minimal number of singular fibers of such fibrations is
equal to $2g+4$ for even $g\geq4$. For odd $g\geq7$, we show that the number is
greater than or equal to $2g+6$. Moreover, we discuss the minimal number of
singular fibers in all hyperelliptic Lefschetz fibrations over the $2$-sphere
as well.
