In the standard Big Bang nucleosynthesis (SBBN) model, the lithium puzzle has attracted intense interest over the past few decades, but still has not been solved. Conventionally, the approach is to include more reactions flowing into or out of lithium, and study the potential effects of those reactions which were not previously considered. 7Be(d, 3He)6Li is a reaction that not only produces 6Li but also destroys 7Be, which decays to 7Li, thereby affecting 7Li indirectly. Therefore, this reaction could alleviate the lithium discrepancy if its reaction rate is sufficiently high. However, there is not much information available about the 7Be(d, 3He)6Li reaction rate. In this work, the angular distributions of the 7Be(d, 3He)6Li reaction are measured at the center of mass energies Ecm = 4.0 MeV and 6.7 MeV with secondary 7Be beams for the first time. The excitation function of the 7Be(d, 3He)6Li reaction is first calculated with the computer code TALYS and then normalized to the experimental data, then its reaction rate is deduced. A SBBN network calculation is performed to investigate its influence on the 6Li and 7Li abundances. The results show that the 7Be(d, 3He)6Li reaction has a minimal effect on 6Li and 7Li because of its small reaction rate. Therefore, the 7Be(d, 3He)6Li reaction is ruled out by this experiment as a means of alleviating the lithium discrepancy.