The infrared spectrum of mass selected Li(+)-D(2) cations is recorded in the D-D stretch region (2860-2950 cm(-1)) in a tandem mass spectrometer by monitoring Li(+) photofragments. The D-D stretch vibration of Li(+)-D(2) is shifted by -79 cm(-1) from that of the free D(2) molecule indicating that the vibrational excitation of the D(2) subunit strengthens the effective Li(+)cdots, three dots, centeredD(2) intermolecular interaction. Around 100 rovibrational transitions, belonging to parallel K(a)=0-0, 1-1, and 2-2 subbands, are fitted to a Watson A-reduced Hamiltonian to yield effective molecular parameters. The infrared spectrum shows that the complex consists of a Li(+) ion attached to a slightly perturbed D(2) molecule with a T-shaped equilibrium configuration and a 2.035 A vibrationally averaged intermolecular separation. Comparisons are made between the spectroscopic data and data obtained from rovibrational calculations using a recent three dimensional Li(+)-D(2) potential energy surface [R. Martinazzo, G. Tantardini, E. Bodo, and F. Gianturco, J. Chem. Phys. 119, 11241 (2003)].