Abstract: Three-way spacecraft Doppler tracking is currently widely used and it plays an important role in the control and navigation of deep space missions. Using the theory of three-way Doppler tracking, including possible violations of the local Lorentz invariance (LLI) and the local position invariance (LPI), we analyzed the post-fit residuals of three-way Doppler tracking data of Mars Express. These Doppler observations were carried out from August 7th to 8th in 2009, with an uplink station administered by the European Space Agency at New Norcia in Australia and three downlink stations at Shanghai, Kunming and Urumqi in China. We find that, although these observations impose preliminary bounds on LLI at the level of 10^-2, they are not suitable for testing LPI because of the configuration of these stations and the accuracy of the observations. To our knowledge, this is one of the first attempts in China to apply radio science to the field of fundamental physics.