In this paper, a terahertz (THz) dual-band bandpass filter based on spoof surface plasmon polaritons (SSPPs) with wide upper stopband suppression is proposed. The filter utilizes two types of hybrid SSPP unit cells loaded on a double-sided quasi-SSPPs transmission line to achieve dual-band filtering responses and wide upper stopband suppression simultaneously. The performance and bandwidth of the filter's passbands can be adjusted by modifying the SSPP unit cells within the dual-band filtering part. The detailed design method is provided to enhance understanding of the operating principle of the presented filter. The simulation results of the designed THz filter demonstrate its excellent dual-band filtering performance. It features a wide stopband spanning from 1.53 to 4.64 THz, effectively suppressing out-of-band signals with S21 < -55 dB in the frequency range of 1.63 to 2.57 THz. To validate the proposed approach, a microwave filter with a similar design is implemented. Finally, the simulated and measured S-parameter responses of the filter are provided for comparison and evaluation.