The current understanding is that the progress of terahertz technology demands highly-functional and high-performance optical devices. Materials are limited in naturally-occurring materials with positive refractive indices when conventional techniques design the devices. However, metamaterial techniques can shed light on a variety of potential applications because a refractive index including a negative one is arbitrarily controlled by various subwavelength structures. Here, inspired by novel fabrication techniques of micron-scale structures, we design a negative refractive index by a metal-slit array with three-dimensional metal microcoils in a terahertz frequency. The parallel-plate waveguide under a cutoff frequency can produce a negative permittivity, and the resonance of the sprit-ring resonators can also produce a negative permeability. An effective negative refractive index with n_eff = -6.9 + j1.1 is designed at 0.26 THz by an approximate analysis with periodic boundary walls, and performance with n = -3.2 at 0.30 THz is visually confirmed by a full model analysis. A time-consuming procedure in the iterative design of the full model can be drastically escaped by initial parameters which is obtained by the approximate model. The structure with the negative refractive index would be applied to many progressive devices, such as bandpass filters, superlenses, and antennas.