We performed 185/187 Re nuclear quadrupole resonance (NQR) measurements under pressure to investigate the superconducting properties of noncentrosymmetric superconductor Cd2Re2O7 under various crystal structures. The pressure dependence of superconducting transition temperature Tc determined through ac susceptibility measurements is consistent with the results of previous resistivity measurements [T. C. Kobayashi etal., J. Phys. Soc. Jpn. 80, 023715 (2011).]. Below 2.2 GPa, in the nuclear spin-lattice relaxation rate 1/T1, a clear coherence peak was observed just below Tc, indicating conventional s-wave superconductivity. In contrast, the coherence peak disappears at 3.1 GPa, suggesting a change in superconducting symmetry to the p-wave dominant state against pressure.