A novel partial negative curvature anti-resonance hollow-core terahertz waveguide is proposed. The waveguide cladding consists of two parts, one part is composed of a dielectric circular tube, which provides a part of the negative curvature boundary for the core; the other part is composed of a plurality of rectangular dielectric layers, and multiple dielectric layers for reducing confinement loss. This waveguide structure does not introduce a new cladding node while adding anti-resonant layers, and it is easy to achieve broadband low-loss transmission of terahertz waves. The full vector finite element method is used for the numerical simulation of the waveguide, and the broadband low loss characteristic is investigated. Based on the simulation analysis, the designed waveguide is printed via 3D printing technology, and the transmission characteristics are tested using a terahertz time-domain spectroscopy system. Experimental results show that the transmission loss of this negative curvature anti-resonance terahertz waveguide is less than 10 dB/m in the range of 0.29~0.42 THz, which is in good agreement with the numerical simulation.