The bremsstrahlung process is studied in complex plasmas including the influence of ions and variable dust charge. The electron-dust particle bremsstrahlung radiation cross-section (e-D-BRCS) is obtained with the analytic expression for the effective dust charge in terms of the Debye length and the temperature ratio. The e-D-BRCS is found to be reduced with either the decrease of ion temperature or increase of electron temperature. The ion density effect is found to be more important in the small electron temperature domain. Interestingly, the influence of ion temperature and density is found to be independent of the bremsstrahlung emission energy. The effective dust charge is also found to decrease with an increase of the ratio of the electron temperature to the ion temperature. In addition, it is found that the effective dust charge increases with an increase of the ratio of the electron density to the ion density. Moreover, the e-D-BRCS is found to be increased with the decrease of ion density.
