We have made ultrasonic measurements on a filled skutterudite PrOs4Sb12 showing a heavy fermion superconductivity at T-C = 1.85 K. The softening of the elastic constant with decreasing temperature has been found above T-C. The (C-11 - C-12)/2 in applying magnetic fields along the [110] axis at 1.0 K exhibits a minimum around 8 T, which is well accounted for by the one-ion quadrupolar susceptibility reflecting the level crossing of one of an excited Gamma(4)((2)) triplet to a ground state Gamma(1) singlet. The softening of (C-11 - C-12)/2 proportional to reciprocal temperature just above T-C may be dominated by the tunneling of an off-center Pr-ion in an Sb-icosahedron cage.