We develop a strong-coupling theory for the superfluidity of fermion pairing phase in a Bose-Fermi mixture. Dynamical screening, self-energy renormalization, and a pairing gap function are included self-consistently within the adiabatic limit (i.e., the phonon velocity is much smaller than the Fermi velocity). An analytical solution for the transition temperature () is derived within reasonable approximations. Using typical parameters of a mixture, we find that the calculated is several times larger than that obtained in the weak coupling theory, and can be up to several percent of the Fermi temperature.