Topological insulators with broken time-reversal symmetry and the Fermi level within the magnetic gap at the Dirac cone provides exotic topological magneto-electronic phenomena. Here, we introduce an improved magnetically doped topological insulator, Fe-doped BiSbTe2Se (Fe-BSTS) bulk single crystal, with an ideal Fermi level. Scanning tunneling microscopy and spectroscopy (STM/STS) measurements revealed that the surface state possesses a Dirac cone with the Dirac point just below the Fermi level by 12 meV. The normalized dI/dV spectra suggest a gap opening with Δmag ~55 meV, resulting in the Fermi level within the opened gap. Ionic-liquid gated-transport measurements also support the Dirac point just below the Fermi level and the presence of the magnetic gap. The chemical potential of the surface state can be fully tuned by ionic-liquid gating, and thus the Fe-doped BSTS provides an ideal platform to investigate exotic quantum topological phenomena.