A comprehensive, calculated line list of frequencies and transition probabilities for the singly deuterated isotopologue of H_3_^+^, H_2_D^+^, is presented. The line list, called ST1, contains over 22 million rotational-vibrational transitions occurring between more than 33 thousand energy levels; it covers frequencies up to 18500cm-1. All energy levels with rotational quantum number, J, up to 20 are considered, making the line list useful for temperatures up to at least 3000K. About 15% of these levels are fully identified with six rotational and vibrational quantum numbers. The list is calculated using a previously proposed, high accuracy, ab initio model and consistency checks are carried out to test and validate the results. These checks confirm the accuracy of the list. A temperature-dependent partition function, valid over a more extended temperature range than those previously published, and cooling function are presented.