In this work, a hollow-core anti-resonant terahertz (THz) fiber with elliptical cladding and nested tubes is proposed and fabricated. It is an effective way to reduce the loss of THz waves by transmitting them in an air core and breaking the material absorption. After parameter optimization of the initial structure, multiple transmission windows exist in the 0.2-0.8 THz band, where confinement loss is as low as 3.47×10-3cm-1 at 0.8 THz. At 0.2-0.7 THz, confinement losses lie between 10-3 and 10-2cm-1. The 3D printed samples are characterized by a THz time-domain spectroscopy system. Experimental results showed that the designed fiber structure transmits loss coefficients up to 10-2cm-1 in the 0.2-0.8 THz band (the minimum value is located at 0.46 THz, corresponding to a loss coefficient of 0.0284cm-1). The experiments show that the designed THz fiber achieves a good transmission effect.