Photonic Crystal Fiber (PCFs) with H-shaped core has been investigated. The PCFs structure consists of six elliptical holes of three different areas. The arrangement of elliptic shaped holes are made such that, it forms an H-shaped core. The simulated results shows the fiber to be highly birefringent. The order of birefringence reported is of 102 order. Dispersion observed by the designed fiber shows anomalous behavior. At all the four optical windows, reported dispersion is below 22ps / nm — km. It is to be noted that the maximum power has been confined at the core of the fiber. Besides the other propagation characteristics of fiber has also been investigated.