Photonic crystal fibers (PCFs) are divided into two different kinds of fibers. The first one, index-guiding PCF, guides light by total internal reflection between a solid core and a cladding region with multiple air-holes. On the other hand, the second one uses a perfectly periodic structure exhibiting a photonic band-gap (PBG) effect at the operating wavelength to guide light in a low index core-region. A compact 2D-FDTD method based on finite-difference time-domain method is formulated and is effectively applied to analysis PCFs and PBGFs. We study the propagation features of fundamental mode and the fundamental characteristics such as effective index, modal-field diameter and chromatic dispersion in index-guiding PCFs. By optimizing the air-hole diameters and the hole-to-hole spacing of index-guiding PCFs, both the dispersion and the dispersion slope can be controlled in a wide wavelength range. We also investigate the propagation features of fundamental mode and band-gap effect of PBGFs.