Photonic crystal fibers with an air hole in the core are analyzed by finite-element method. The relations of mode field distribution, confinement loss and dispersion characteristics with fiber structure parameter and wavelength are achieved. The principle of guiding light in air hole is explained by diffraction and the characteristics of photonic crystal fiber. For the fiber with low loss, single-mode, tightly confined light in the air core, the ranges of structure parameters and wavelengths are obtained. An optimal fiber structure is designed, of which the mode is tightly confined in the air core, and the confinement loss α=5.9× 10-5 dB/km. These provide theoretical instruction for the design and fabrication of photonic crystal fiber with an air hole in the core. The high intensity in an air hole, coupled with long interaction length, promises a new class of experiments in light-matter interaction and nonlinear fiber optics.