General relativity (GR) predicts that photons are delayed and deflected by the space curvature produced by any mass. The Post-Newtonian (PN) parameter controlling the curvature induced by a gravitational field is γ, with bending and delay effects proportional to (γ + 1). γ = 1 in GR. The most accurate estimation of this PN parameter γ = (1 + (2.1 ± 2.3)) · 10-5, has been obtained by the NASA mission Cassini [1] exploiting the frequency shift of radio signal during a Superior Solar Conjunction (SSC) in 2002, while the spacecraft was in cruise to Saturn. The crucial element of the experiment was an advanced radio system providing a highly stable multi-frequency radio link in X and Ka band (8.4 and 32.5 GHz), and a nearly complete cancellation of the plasma noise introduced by the solar corona in Doppler measurements. The ESA-JAXA mission BepiColombo to Mercury will improve the Cassini radio instrumentation by enabling the ranging function also in the Ka band radio link used by the Mercury Orbiter Radio science Experiment (MORE). The fully digital architecture of the transponder provides a pseudo-noie modulation of the carrier at 24 Mcps and a two-way range accuracy of 20 cm. Thanks to the simultaneous tracking by means of the standard telecommunication link, both range and range rate observables will be available for new, more accurate tests of GR. This paper reports on the simulations carried out in order to assess the attainable accuracies in the estimation of γ during the cruise phase of BepiColombo. In an optimal configuration, an uncertainty of 5·10-6 may be attained. © 2015 IEEE.