Using plane wave expansion (PWE) method, four kinds of promising two-dimensional (2D) photonic crystals including square air holes, hexagonal air holes, square rods and hexagonal rods aiming at short-wavelength light emitting diode (LED) are studied. Transverse electric (TE) and transverse magnetic (TM) photonic band gaps (PBGs) are calculated under different lattice constants with different air filling fractions (AFFs) and ratios of pillar radius to lattice constant. The analysis of data indicates that the center wavelength of PBG increases with smaller AFF. Compared with other structures, the structure with square rods has more potential in improving the extraction efficiency of short-wavelength LED, while those with hexagonal rods and hexagonal air holes are suitable for structuring short-wavelength polarization LED.