We present the results of the first three-dimensional (3-D) simulation of the water isotope HDO in the Martian atmosphere. This deuterated isotope of water has long been used on both Earth and Mars as a proxy to understand the climatic evolutions of these planets. On Mars, the current enrichment in deuterium concentration in the atmosphere is believed to be indirect evidence of a wetter climate in the past. Due to its vapor pressure being lower than that of H2O, HDO gets fractionated at condensation and therefore concentrates in the Martian water ice clouds. Our study aims at understanding the latitudinal, vertical, and temporal variations of this species under current Martian climate. Our results indicate that the globally averaged D/H ratio in the Martian atmosphere should vary modestly with season, with changes on the order of 2%. Locally, however, this same ratio exhibits large annual changes (by a factor of 2) in the high-latitude regions. These fluctuations are controlled by the Polar Hood water ice clouds, within which HDO gets heavily fractionated. Due to the combined action of summer clouds above the north polar cap and to the cold-trapping effect of the south residual cap, the global atmospheric deuterium concentration is predicted to be more than 15% lower than the concentration in the north permanent cap ice. We thus extrapolate by suggesting that the true D/H ratio of Martian water may exceed 6.5 (wrt. SMOW), rather than the 5.6 inferred from atmospheric probing. The globally and annually averaged vertical distribution of HDO exhibits a mild decline with altitude, a result in significant contrast with previous 1-D studies. These results will help constrain more accurately the photochemical models aimed at understanding the observed low concentration of deuterium at high altitudes and thus the process of water escape to space.