We propose a porous polymer terahertz fiber with a core composed of a hexagonal array of subwavelength air holes. Numerical simulations show that the larger part of guided power propagates inside the air holes within the fiber core, resulting in suppression of the bulk absorption losses of the core material by a factor of ∼10–20. Confinement of terahertz power in the subwavelength holes greatly reduces effective refractive index of the guided mode but not as much as to considerably increase modal radiation losses due to bending. As a result, tight bends of several centimeter bending radii can be tolerated.