The plane-wave expansion method is used to calculate the band structure of a two-dimensional photonic crystal formed by a triangular lattice of anisotropic elliptic cylinders. After optimizing the parameters of the elliptic cylinders, we find a large bandgap (about 0.0449 ωe, ωe ＝ 2πc/a) at high frequencies beside a coexisting large absolute gap (about 0.035 ωe) at low frequencies. Numerical results show that the optimal design is very stable under any parameter perturbation.