Compared with the photonic crystal (PC) structures composed of Si circular, the PC structrures composed of triangular lattice of air holes in a dielectric slab are more easily fabricated and integrated. The tunability of directional band gap in a two-dimensional photonic crystal of air holes in a semiconductor matrix is demonstrated numerically, using the plane wave expansion calculation. Numerical simulations show that the photonic crystal band gaps are modulated by nematic liquid crystals infiltrated in the air holes. Then the band gap can be controlled easily under the influence of the external electric field. So the results can serve as a field-sensitive polarizer. These results are in agreement with that of Liu. However, the tunable field-sensitive polarizer based on the phenylacetylene liquid crystals instead of 5CB liquid crystals has the wider frequency range. Moreover, the transmission spectrum of the photonic crystal infiltrated by liquid crystal is analyzed, using finite difference time domain (FDTD) method. Numerical simulations show that the shift of the spectrum modulated by liquid crystal can be used to design a novel switch.