Pressure effect on superconductivity in Cd2Re2O7

188/187Re nuclear quadrupole resonance (NQR) and ac susceptibility measurements in Cd2Re2O7 have been performed to study correlation between superconductivity and structural transition (Ts1 = 200 K and Ts2 = 120 K at ambient pressure) under high pressure, using a hybrid piston cylinder-type high-pressure cell. Tc is almost pressure independent below 1 GPa, while, above 1 GPa, Tc increases monotonously and reaches up to 2.3 K at 2.5 GPa. The 188/187Re-NQR spectrum for ±3/2 ↔ ±5/2 transition broadens and shifts to lower frequency with applying pressure. Furthermore, Re NQR spectrum broadens suddenly around 2GPa, suggesting that electric field gradient at Re sites distributes extendedly, which may be related to the disorder state with suppressing Ts2 down to ~ 0 K.