The Dirac_Slater method is used to calculate the photoionization cross sections of Bi79+ from low to high energy. The numerical results are compared with those calculated by the quasi_classical Kramers formula, and the validity of Kra mers formula is analyzed. The relativistic effects and multipole contributions o f the photoionization processes are also discussed. For the comparison with the merged_beam rate coefficients, the theoretical rate coefficients were evaluated with the experimental electron_velocity distribution function(characterized by t he temperatures) parallel and perpendicular to the electron_beam direction. Thou gh the effects of relativity are considered in the present work, the measured ra te coefficients exceed our results in the energy range close to the threshold.