The triply degenerate stretching (nu(3)) and bending (nu(4)) modes of CD4 in solid parahydrogen at cryogenic temperatures are studied by Fourier transform infrared spectroscopy to reveal crystal field split rovibrational structures. The observed spectra are analyzed by taking into account the crystal field potential which is constructed by the summation of the pairwise (dispersive) potential between the methane and the surrounding hydrogen molecules. By the least-squares fitting of that observed to a theoretical model the molecular constants of CD4 as well as the potential coefficient are determined as in the previous work on the CH4/p-H-2 system. The potential is approximated to be proportional to the product of the polarizability of hydrogen molecule, the dipole-quadrupole polarizability of methane, and the inverse of the seventh power of the intermolecular distance between methane and hydrogen molecules. From the ratio of the potential coefficients of CH4 and CD4 the dipole-quadrupole polarizability of CD4 is found to be 0.875 times that of CH4 under the assumption that the quantum renormalization effect is negligible. A novel temperature dependence of the line shape of the nu(3) and nu(4) modes is discovered over the range of 4.5 to 8.0 K.