  Applying electric or magnetic fields is widely used to not only create and
manipulate topological states but also facilitate their observations in
experiments. In this work, we show by first-principles calculations and
topological analysis that the time-reversal (TR) symmetry-broken quantum spin
Hall (QSH) state emerges in a two-dimensional ferromagnetic MnBi$_4$Te$_7$
monolayer. This TR-symmetry broken QSH phase possesses a highly tunable
nontrivial band gap under an external electric field (or tuning interlayer
distance). Furthermore, based on the Wannier-function-based tight-binding
approach, we reveal that a topological phase transition from the TR-symmetry
broken QSH phase to the quantum anomalous Hall (QAH) phase occurs with the
increase of magnetic fields. Besides, we also find that a reverse electric
fields can facilitate the realization of QAH phase. Our work not only uncovers
the ferromagnetic topological properties the MnBi$_4$Te$_7$ monolayer tuned by
electric and magnetic fields, but also can stimulate further applications to
spintronics and topological devices.
