Primordial 7Li abundance inferred from observations of metal-poor stars is a factor of about 3 lower than the theoretical value of standard big bang nucleosynthesis (BBN) model. One of the solutions to the Li problem is 7Be destruction during the BBN epoch caused by a long-lived negatively charged massive particle, X-. The particle can bind to nuclei, and X-bound nuclei (X-nuclei) can experience new reactions. The radiative X- capture by 7Be nuclei followed by proton capture of the bound state of 7Be and X- (7Bex) is a possible 7Be destruction reaction. Since the primordial abundance of 7Li originates mainly from 7Li produced via the electron capture of 7Be after BBN, the 7Be destruction provides a solution to the 7Li problem. We suggest a new route of 7Bex formation, that is the 7Be charge exchange at the reaction of 7Be3+ ion and X-. The formation rate depends on the ionization fraction of 7Be3+ ion, the charge exchange cross section of 7Be3+, and the probability that excited states 7Bex* produced at the charge exchange are converted to the ground state. We find that this reaction can be equally important as or more important than ordinary radiative recombination of 7Be and X-. The effect of this new route is shown in a nuclear reaction network calculation.