The European Space Agency Gaia satellite, planned for launch in late 2013, will perform systematic astrometric observations of the whole sky over a five year period. During this mission many thousands of Solar System Objects down to magnitude V = 20 will be observed including Near-Earth Asteroids and objects at Solar elongations as low as 45 • , which are difficult to observe with ground-based telescopes. We simulated the detection of Trojan asteroids in the orbits of Earth and Mars by Gaia. We find that Gaia will not detect the Earth Trojan 2010 TK 7 although it will detect any Earth Trojans with diameters larger than 600 m. We also find that Gaia will detect the currently known Mars Trojans and could discover more than 100 new Mars Trojans as small as 400 m in diameter. The results of the Gaia mission will test the predictions about the Mars Trojan asteroid population and lead to greater understanding about the evolution of the Solar System.