Solar System tests of a brane world, which is called DMPR model, were studied in recent works. The correction of DMPR model to the general relativity (GR) in the four-dimensional curved spacetime can be parametrized by a "tidal charge" parameter Q. The parameter Q in this model was obtained and improved as vertical bar Q vertical bar less than or similar to 6.7 m(2) by the Earth-Mercury ranging. A new test of the DMPR model based on gravitational time advancement is proposed and investigated in this work. The advancement is a gravitational consequence on round-trip proper time duration of a photon. For ranging a distant spacecraft, it is shown that (1) the "tidal charge" parameter can make the advancement larger or smaller than the one of GR, depending on the sign of Q; (2) the superior conjunction (SC) and the inferior conjunction (IC) are all suitable for detecting the advancement; (3) the advancement can be complementary to the classical test of Shapiro time delay for detecting the brane world; and (4) the implementation of optical clocks and planetary laser ranging will provide more insights on the brane world model in the future.