A novel method to realize stopband within the operating frequency of spoof surface plasmon polaritons (SPPs) is presented. The stopband is introduced by a new kind of capacitive-coupled series spoof SPPs. Two conventional H-shaped unit cells are proposed to construct a new unit cell, and every two new unit cells are separated by a gap with certain distance, which is designed to implement capacitive coupling. The original surface impedance matching is disturbed by the capacitive coupling, leading to the stopband during the transmission of SPPs. The proposed method is verified by both numerical simulations and experiments, and the simulated and measured results have good agreements. It is shown that the proposed structure exhibits a stopband in 9-9.5 GHz while the band-pass feature maintains in 5-9 GHz and 9.5-11 GHz. In the passband, the reflection coefficient is less than -10 dB, and the transmission loss is around 3 dB; in the stopband, the reflection coefficient is -2 dB, and the transmission coefficient is less than -30 dB. The compact size, easy fabrication and good band-pass and band-stop features make the proposed structure a promising plasmonic device in SPP communication systems.