This paper proposes a hexagonal photonic crystal fiber (H-PCF) structure with all circular air holes in order to simultaneously achieve ultrahigh birefringence and high nonlinearity. The H-PCF design consists of an asymmetric core region, where one air hole is a reduced diameter and the air hole in its opposite vertex is omitted. The light-guiding properties of the proposed H-PCF structure were studied using the full-vector finite element method (FEM) with a circular perfectly matched layer (PML). The simulation results showed that the proposed H-PCF exhibits an ultrahigh birefringence of 3.87 × 10−2, a negative dispersion coefficient of −753.2 ps/(nm km), and a nonlinear coefficient of 96.51 W−1 km−1 at an excitation wavelength of 1550 nm. The major advantage of our H-PCF design is that it provides these desirable modal properties without using any non-circular air holes in the core and cladding region, thus making the fiber fabrication process much easier. The ultrahigh birefringence, large negative dispersion, and high nonlinearity of our designed H-PCF make it a very suitable candidate for optical backpropagation applications, which is a scheme for the simultaneous dispersion and nonlinearity compensation of optical-fiber transmission links.