We report evidence for a structural phase transition in individual suspended metallic carbon nanotubes by examining their Raman spectra and electron transport under electrostatic gate potentials. The current-gate voltage characteristics reveal anomalously large quasi-metallic band gaps as high as 240 meV, the largest reported to date. For nanotubes with band gaps larger than 200 meV, we observe a pronounced M-shape profile in the gate dependence of the 2D band (or G' band) Raman frequency. The pronounced dip (or softening) of the phonon mode near zero gate voltage can be attributed to a structural phase transition (SPT) that occurs at the charge neutrality point (CNP). The 2D band Raman intensity also changes abruptly near the CNP, providing further evidence for a change in the lattice symmetry and a possible SPT. Pronounced non-adiabatic effects are observed in the gate dependence of the G band Raman mode, however, this behavior deviates from non-adiabatic theory near the CNP. For nanotubes with band gaps larger than 200 meV, non-adiabatic effects should be largely suppressed, which is not observed experimentally. This data suggests that these large effective band gaps are primarily caused by a SPT to an insulating state, which causes the large modulation observed in the conductance around the CNP. Possible mechanisms for this SPT are discussed, including electron-electron (e.g., Mott) and electron-phonon (e.g., Peierls) driven transitions.