Photonic edge mode confining light in cavities of surface plasmons is beneficial in image and biosensor applications. In the terahertz band, however, the edge mode in a cavity of spoof localized surface plasmons has not matured sufficiently. Herein, a cost-effective strategy to achieve a terahertz photonic edge mode using a metasurface of strongly coupled fourfold spoof localized surface plasmons in a tetramer layout is demonstrated. The quality factors of edge modes decrease when the tetramer shrinks, as revealed by the terahertz dielectric functions. The edge modes that emerge can be categorized as inner and outer edge modes, as deduced from the simulated electric field distribution. Our results show that the edge modes are due to the interaction of spoof localized surface plasmons in the terahertz band.