Quasi-line waves represent a distinct class of propagation modes along non-complementary impedance surfaces, offering an alternative to the conventional line waves typically formed by complementary impedance surfaces. In this study, we introduce a novel design for quasi-line waves utilizing non-dual, purely inductive impedance structures. By incorporating multilayer graphene, our design achieves wide bandwidth and extended propagation lengths in the terahertz range, with field concentration localized at the edges of the inductive surfaces. This configuration enables unidirectional wave propagation, with graphene integration providing precise control over bandwidth and transmission characteristics. Unlike traditional line waves, which are constrained to specific terahertz frequency ranges, our quasi-line mode-guided by self-inductive impedance surfaces-demonstrates significantly broader bandwidth and enhanced electric field intensity. The performance of this mode is strongly influenced by capacitance variations between impedance surfaces, exceeding the singularity limitation of conventional line waves. Our proposed structure demonstrates superior performance in both bandwidth and mode singularity within the terahertz spectrum, surpassing traditional line wave designs.