In order to explore the properties of photoniccrystals, the finite element method was introduced to calculate the band structure of lossy and dispersive photonic crystals with triangular lattice. By using this method, the calculation of band structure is reduced to a quadratic eigenvalue problem which the eigenvalue is the Bloch wave vector, the band structure and eigenmode can be obtained more effectively. The band structure in the TE and TM mode of photonic crystals with dielectric material in triangular lattice was compared with the reference to demonstrate the accuracy of the method. Furthermore, the dispersion relation of the lossy and lossless photonic crystals was also given by the proposed method. The symmetry and surface plasmon polarizations properties are found in lossless photonic crystals and electric field distributions are concentrated on the interface of dispersive materials and air. It is demonstrated in the lossy photonic crystals that the symmetry is destroyed, the surface plasmon polarizations properties are weakened and electric field density is decreased. The results can be used as theoretical basis and reference for studying the lossy photonic crystals and surface plasmon polarizations.