The photonic crystal fiber is a kind of microstructured optical fiber with a 2-D periodial dielectric profile constructed by air/silica. There are a few models to investigate the mode characteristics. For the TIR PCF, as an example, the index profile can be considered as the construction of a pure center defect and a perfect 2-D photonic crystal with the periodic air-hole lattice, which can be expanded with the normalized Hermite-Gaussian basis set and cosine function respectively. From the electromagnetic wave equation, the mode eigen equation can be obtained with the algorithm when the transverse electric field is also expanded as the series of the Hermite-Gaussian basis. All elements in the eigen equation are evaluated analytically based on the orthonormality and some identities of the Hermite-Gaussian function. The propagation constant and the mode field distribution of the PCF can be calculated, hence the mode characteristics, the dispersion properties and the polarization properties can also be investigated with this algorithm.