In this paper, a novel basic structure of a dual-band bandstop filter (DBSF) without coupled lines is proposed. In order to improve the performance, some optimizations are made to the basic structure, and two DBSF structures with multi-transmission zeros and multi-transmission poles are obtained. These filters have the advantages of simple structure, high selectivity, and high stopband rejection, among which the deepest stopband can be better than 45 dB.In addition, an extraction method of transmission zeros and transmission poles based on the S-parameter theory is proposed. The ideal 3-dB fractional bandwidths of the basic structure are 37.8% and 18.7%, respectively, 54.1% and 25.9% for the first improved structure, respectively, and 75.1% and 34.2% for the second improved structure, respectively. EM simulation results and measured results are highly unified to verify the proposed filter structure.