Two-dimensional photonic crystal possess only pseudo photonic band gaps, so it is interesting and meaningful that whether the spontaneous emission of the atoms in two-dimensional photonic crystals can be controlled effectively. The density of photonic states and local density of photonic states are most important to determine the properties of atomic spontaneous emission. the density of states and local density of states of the two-dimensional photonic crystal composed of air cylinders on square lattice are investigated by plane wave expansion method and group theory. The air cylinder as scatter is positioned on uniform dielectric background, the calculated results show that the density of states and local density of states exhibit nonzero values but evidently lower than those outside the peseudo-gap range in the frequency range of pseudo-gap, and it may be regarded as a quasi-photonic band gap. The local density of states takes much larger values in the air cylinders areas and drops down at the boundary between the air cylinders and dielectric medium background, and this phenomenon is due to the continuity of electric displacement vector. Considering that the above two characteristics are also found in other two-dimensional photonic crystal sample, it is believed they are universal in two-dimensional photonic crystal.