Constant-frequency　contours　analysis　method　and　the　plane-wave　method　were　employed　to　gain　the　frequency　range　of　the　incident　electromagnetic　waves　when　all-angle　negative　refraction　(AANR)　phenomenon　occurs　in　two-dimensional　photonic　crystals.　The　dependence　of　the　frequency　range　on　structural　parameter　(crystal　lattice　shape,　the　ratio　of　the　rod　radius　and　the　lattice　constant)　and　electromagnetic　parameter　(the　dielectric　constants　of　the　rods　and　of　the　background,　incident　electromagnetic　waves　with　different　polarization)　were　investigated.　The　result　shows　that　when　a　dielectric　constant　is　fixed,　it　is　necessary　that　the　other　dielectric　constant　reach　a　threshold.　Photonic　crystal　has　its　optimized　structural　parameter　and　electromagnetic　parameter　when　it　has　its　largest　AANR　frequency　range.