We report Sb-123 nuclear quadrupole resonance (NQR) measurements of the filled skutterudite heavy-fermion superconductor PrOs4Sb12 under high pressures of 1.91 and 2.34GPa. The temperature dependence of NQR frequency and the spin-lattice relaxation rate 1/T-1 indicate that the crystal-electricfield splitting Delta(CEF) between the ground state Gamma(1) singlet and the first excited state Gamma((2))(4) triplet decreases with increasing pressure. The 1/T-1 below T-c = 1.55 K at P = 1.91 GPa shows a power-law temperature variation and is proportional to T-5 at temperatures considerably below T,, which indicates the existence of Point nodes in the superconducting gap function. The data can be well fitted by the gap model Delta(theta) = Delta(0) sin theta with Delta(0) = 3.08k-B T-c. The relation between the superconductivity and the quadrupole fluctuations associated with the 1,(2) state is discussed.