We investigated the pressure dependence of electric transport in a superconducting sample, Ba0.77Na0.23Ti2Sb2O, to complete the phase diagram of superconducting transition temperature (T-c) against pressure (p). This superconducting sample exhibits a T-c value of 5.8 K at ambient pressure. Here, the superconductivity of the recently reported sample was investigated over a wide pressure range. The T-c value monotonously decreased with pressure below 8 GPa. Interestingly, the T-c value rapidly increased above 8 GPa and slowly declined with pressure above 11 GPa. Thus, a new superconducting phase was discovered above similar to 9 GPa. The crystal structure of Ba0.77Na0.23Ti2Sb2O was also elucidated at 0-22.0 GPa with synchrotron X-ray powder diffraction. Consequently, an evident relation between the crystal structure and the superconductivity was revealed, namely, a clear structural phase transition was observed at 8-11 GPa, where the T-c value rapidly increased against pressure. This study provides detailed information on the superconductivity of Ba0.77Na0.23Ti2Sb2O under pressure, which will lead to a comprehensive understanding of pressure-driven superconductivity.