Desire for terahertz sophisticated optical devices is rapidly increasing in order to prepare the utilization of higher frequencies, such as terahertz frequencies and optical ranges. However, conventional techniques cannot solve the limitation that devices are designed only by naturally-occurring materials with positive refractive indices. Metamaterials with a negative refractive index can overcome the limitation and provide potential solutions to the demands for novel devices. We design a negative refractive index by a metal-slit array with split-ring resonators in a terahertz frequency. A negative permittivity is designed by a parallel-plate waveguide under a cutoff frequency, and a negative permeability is by the resonance of sprit-ring resonators. An approximate analysis with periodic boundary walls designs an effective negative refractive index with neff = -2.5 + j0.40 at 0.30 THz, and a full model analysis visually confirms performance with n = -2.6 at 0.30 THz. The approximate model can drastically reduce a time-consuming design procedure and simultaneously prepare initial parameters for the full model analysis. The proposed design model with the negative refractive index would lead to potential applications, such as bandpass filters with a high extinction ratio in undesired frequency bands and superlenses overcoming a diffraction limit.