This paper describes a theoretical study of the lowest-order transverse electric (TE₁) mode of a terahertz parallel-plate metal waveguide, and an approximate expression for the effective refractive index of the TE₁ mode of the terahertz parallel-plate metal waveguide is derived under the condition of real metal parameters. First, the TE₁ mode is numerically simulated based on the finite element method, and the simulation results are compared with the values obtain from the approximate expressions to verify the feasibility of the theoretical derivation. The error analysis shows that the deduced approximate expression has high accuracy in the entire terahertz band and exhibits the characteristics of a wide range of applicable frequencies. Simulation results show that this approximate expression has a high degree of applicability to the analysis of the TE₁ mode and will promote the research and application of parallel-plate metal waveguides.