Large-mode-area single-mode fibers play an important role in the field of high power lasers, high power delivery, and high sensitivity sensor. A novel all-solid large-mode-area single-mode photonic quasi-crystal fiber with extremely low loss is proposed. This kind of fiber contains a hexagonal quasi-crystal array of slightly fluorine-doped silica rods in a silica background. Its structure and properties are simulated numerically in virtue of finite element method. Effects of variation of d/Λ, or Λ on fiber loss and effective mode-area properties are investigated. Numerical results demonstrate that an effective mode-area of 5197 μm2, low confinement loss of 10-5 dB/km for fundamental mode and high confinement loss of 100 dB/km of second-order mode at a wavelength of 1064 nm. Numerical simulations show that this fiber can operate effectively in single-mode and remove the conflict between large-mode-area and low loss. Moreover, the bending loss for a bending radius of 10 cm is as low as 0.01 dB/m. This fiber can increase the thermal damage threshold of the PQF, decrease the coupling loss and simplify the fabrication process. The design of new fibers is highly meaningful for the development of high power delivery, fiber lasers, and fiber amplifiers.