The band gap structure of one-dimensional anisotropic photonic crystal has been studied by means of the transfer matrix formalism. From the analytic expressions and numeric calculations we see some general characteristics of the band gap structure of anisotropic photonic crystals, each band separates into two branches and the two branches react to polarization sensitively. In the practical case of oblique incidence, gaps move towards high frequency when the angle of incidence increases. Under some special conditions, the two branches become degenerate again.