The J = 2 ← 1 and 3 ← 2 rotational transitions of AlD (X1Σ+) near 393 and 590 GHz have been measured using submillimeter direct absorption spectroscopy. AlD was created in an AC discharge of Al(CH3)3 and D2 in the presence of argon. This work is the first direct measurement of the J = 3 ← 2 transition of AlD. Each transition was found to be split into multiple hyperfine components due to the 27Al nuclear spin of I = 5/2, some of which are blended together. The data for AlD were fit with an effective Hamiltonian and rotational, electric quadrupole, and nuclear spin-rotation constants were determined for the molecule. The accuracy of these constants has been improved by a factor of 2–3, compared to previous studies. From these data, predictions for the J = 1 → 0 and 4 → 3 transitions of AlD have also been made. Photospheric AlH has been observed via its A1Π-X1Σ+ electronic transition, suggesting that this species may be present in circumstellar gas surrounding late-type stars, where four aluminum-bearing molecules have already been detected. High deuterium enrichment has been observed in hydride species in molecular clouds, making AlD a feasible candidate for searches in these objects as well.