A dynamically tunable terahertz metamaterial structure, comprising a split ring resonator made of lossy metal and a graphene formed square ring resonator, is designed and proposed. Subsequently, the influence of geometrical parameters of the proposed metamaterial structure and electromagnetic properties of graphene on the tunable terahertz spectral characteristics are investigated in detail. Meanwhile, the use of the equivalent model can provide numerical alternative methods and theoretical support for the design, optimization, simulation, and verification of metamaterial devices. The performances of the unit cell and the metamaterial are studied by a coupled oscillator model and a semi-analytical transmission line model; the analytic results agree excellently with our numerical results using full-wave simulations. The dynamical adjustment capacity of terahertz transmission spectra depends on the tunable terahertz metal-graphene hybrid metamaterial, which allows for designing an efficient device for a wide range of specific tasks including applications in sensing and switching. Furthermore, a comprehensive analytical approach based on these models constructs a theoretical basis for the design of metamaterial structures in a wider range and supports the mutual verification of the fitting results.