We propose a novel single polarization photonic band gap fiber (SP-PBGF) with an anisotropic air hole lattice in the core. An SP-PBGF with an elliptical air hole lattice in the core recently proposed can easily realize SP guidance utilizing the large difference of cutoff frequency for the x- and y-polarized modes. In this paper, in order to achieve SP guidance based on the same principle of this PBGF, we utilize an anisotropic lattice of circular air holes instead of elliptical air holes to ease the fabrication difficulty. After investigating the influence of the structural parameters on SP guidance, it is numerically demonstrated that the designed SP-PBGF has 381 nm SP operating band.