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A new superconducting sample, Ba1−xCsxTi2Sb2O, was prepared and characterized in a wide pressure range. The maximum value of superconducting transition temperature, Tc, of Ba1−xCsxTi2Sb2O was 4.4 K for x = 0.25 at ambient pressure. The crystal structure was determined to be tetragonal [space group of P4/mmm (No. 123)]. The charge density wave/spin density wave transition was observed at 44 K for Ba1−xCsxTi2Sb2O (nominal x = 0.25) at ambient pressure, but the transition was suppressed by applying pressure. The pressure dependent X-ray diffraction showed no structural phase transition up to 23.4 GPa, but very interesting Tc–pressure (p) behavior was observed, i.e. the Tc decreases with an increase in pressure up to 4.0 GPa, but it increased above 4.0 GPa, suggestive of non-BCS type behavior. Thus, the systematic study on new pnictide superconductor, Ba1−xCsxTi2Sb2O, was achieved, and the fascinating behavior of superconductivity against pressure was discovered. [ABSTRACT FROM AUTHOR]