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 +-D 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)].