In the terahertz communication and imaging systems, terahertz fibers have aroused great interest in the past several years. Countering the terahertz wave applications ‘inefficient transmission’ calls for a rapid development in terahertz fibers that could achieve low confinement loss, chromatic dispersion and large refraction of power at the same time. In this paper, a new type of negative curvature terahertz fiber is designed, which consists of six cladding tubes evenly distributed in the cladding and nested with equilateral triangle structure. By using full vector finite element method and changing the thickness of cladding tube and triangle, the effective mode field area, core power ratio, confinement loss, dispersion and other parameters of negative curvature fiber are studied. Here, the thickness range of 70–100 μm is selected. It is found that the confinement loss of optical fiber can reach 0.005 dB/cm at 2.36 THz, the dispersion coefficient can float up and down at ±0.1 ps/(THz·cm) at the frequency range of 2.1–2.8 THz, the core power ratio can reach above 99% in the same frequency range. Compared with the known terahertz negative curvature fiber, the nested triangle negative curvature fiber has lower confinement loss and wide transmission bandwidth of 2.1–2.8 THz. After that, when the cladding tube and the triangle thickness are kept at 90 μm, the bending degree of the triangle edge is changed, and the above properties are further studied. When the triangle edge is bent in and out, the transmission performance of the fiber is analyzed. It is found that when the triangle edge is bent inward, the transmission characteristics of terahertz wave is much better than that when the triangle edge is bent outward. When the triangle edge is bent inwards, the confinement loss is obviously reduced, reaching 0.002 dB/cm at 2.36 THz. Compared with triangle straight edge, the confinement loss is reduced by 40% and still maintaining 99% core power ratio at certain frequency band. The designed terahertz fiber will have an important application value in the fields of sensing and imaging systems with low loss and wide bandwidth. This makes the Topas COC-based terahertz fiber very suitable for guiding terahertz wave over the desired frequency range.