© 2019, The Author(s).Spoof surface plasmon polariton waveguides are perfect candidates to enable novel, miniaturized terahertz integrated systems, which will expedite the next-generation ultra-wideband communications, high-resolution imaging and spectroscopy applications. In this paper, we introduce, for the first time, a model for the effective dielectric constant, which is the most fundamental design parameter, of the terahertz spoof surface plasmon polariton waveguides. To verify the proposed model, we design, fabricate and measure several waveguides with different physical parameters for 0.25 to 0.3 THz band. The measurement results show very good agreement with the simulations, having an average and a maximum error of 2.6% and 8.8%, respectively, achieving 10-to-30 times better accuracy than the previous approaches presented in the literature. To the best of our knowledge, this is the first-time investigation of the effective dielectric constant of the terahertz spoof surface plasmon polariton waveguides, enabling accurate design of any passive component for the terahertz band.