A collisional-radiative model based on the approach of detailed relativistic configurations is developed, where the complete set of atomic data including photo-excitation, photoionization, electron impact excitation, electron impact ionization and autoionization is calculated, and the data of the inverse processes are obtained by detailed balance. The population distribution is obtained by solving the rate equation under the steady-state condition. The present model is applied to calculate the charge state distribution and M band emission spectra of gold plasmas in non-local thermodynamic equilibrium under a variety of plasma conditions. Comparisons between the present work and experimental results were made and good agreement is found. For the strong transition lines, the intensities predicted by the present model agree with those of experimental spectra within 50%. The present work is useful in analyzing and interpreting experiments as well as in diagnosing the electron temperature in experiments.