An isostructural phase transition and a cubic to tetragonal phase transition in spin-frustrated pyrochlore Dy2Ti2O7 (DTO) at 35 GPa and 46 GPa, respectively, were detected by x-ray diffraction (XRD) and Raman spectroscopy studies at room temperature under high pressure. The band gap of DTO gradually increased with the increasing pressure up to 20 GPa, after which it narrowed significantly around 35 GPa, and further manifested with a slight discontinuity around 46 GPa. Below 35 GPa, the evolution of band gap with pressure maintained a close relationship with the Ti-O bond length and the distortion of TiO6 octahedron. The remarkable narrowing of the band gap around 35 GPa implied the changes of the band structure and confirmed the isostructural phase transition. These findings provide an in-depth understanding of the evolution of the structure and the band gap of DTO under high pressure.