We present a novel structure of two-dimensional (2D) hexagon-lattice photonic crystal with asymmetrical scatterers-Taiji-shaped scatterers. The properties of photonic band gap (PBG) and the influence of parameter on absolute photonic band gap are analyzed by plane wave expansion method. The calculation results demonstrate that the reduction of scatterer symmetry can produce an increase in the number of PBG and a broadening of PBG width for both TE and TM model, which is conducive to obtaining wider and more absolute PBG. By optimizing the parameters of structure, we obtain the widest absolute PBG 0.0541(ωa / 2πc) at ε = 17, R= 0.38 μm, r=0.36R, and θ = 0° and the maximum of 8 absolute PBGs at ε = 16, R=0.44, r=0.2R, and θ = 0°.