Compton suppression is a beneficial technique employed in gamma-spectroscopy to decrease the Compton continuum and enhance the detection efficiency for various radionuclide identification/measurement applications. However, for cascade gamma-emitters radionuclides the conventional approach of Compton suppression (i.e., surrounding HPGe with NaI(Tl)/plastic detectors) removes all coincident events and reduces the detection efficiency. In this study, to address this challenge, a new approach is proposed that uses serial geometry (i.e., NaI(Tl) detector + sample + HPGe detector), more accurate coincidence time window, and the recorded gamma-ray energy in the detectors. The approach is experimentally tested and compared with the conventional approach. The results showed that by the proposed approach for 60Co, a cascade gamma-emitter nuclide, the suppression factor (SF) is improved and only 8% of photo-peak events, compared to 25% in the conventional approach, are lost by the suppression procedure. This decrease in loss of the photo-peak events in the proposed Compton suppression approach improves the accuracy of the activity measurement of the cascade-emitter radionuclides.