This paper presents a new type of wideband absorptive bandstop filter (ABSF) design that is capable of absorbing the input power within the stopband at its Port 1. It is achieved by introducing one additional resistor to a conventional wideband stub bandstop filter. Suitable design procedures are established to facilitate the synthesis of the proposed wideband ABSFs with different filter orders and stopband bandwidths. To validate the proposed design method, microstrip ABSF design examples with a stopband center frequency f-0 of 2 GHz and 30-dB stopband bandwidths ranging from 12% to 42% are demonstrated. The measured stopband rejection at f-0 is larger than 60 dB for all design examples. In addition, good input return losses both in the passband and stopband are achieved, and the measured input return loss is better than 10 dB from dc to 2.5f-0. Larger than 90% of the input power within the stopband can thus be dissipated by the proposed ABSF. To the best of our knowledge, these are the ABSFs with the widest stopband bandwidth ever reported.