We have studied the degree of polarization (DOP) and the state of pol arization (SOP) of partially coherent electromagnetic anomalous vortex beam (PCEAVB) through anisotropic non -Kolmogorov atmospheric turbulence.The results show that the distributions of DOP present concentric ri ng,and the number of concentric rings will increase with the increasing of beam order n and topological charge m.And the relative high DOP distribution region tends to the middle region with the increasing of beam order n and the decreasing of topological charge m,otherwise,it tends to the outer ring distributi on.We can also find that the SOP distributions of PCEAVB will change from uniform linear polarization into nonuniform linear polarization with the increasing of propagation distance z,and the polarization angle shows the circular distribution.And the region with large polarization angle gradually moves to the outer ring with the increasing of prop agation distance z.The big polarization angle region of PCEAVB with the bigger topological charge m and smaller beam order n is closer to the central region.Moreover,the larger beam order n and topological charge m,the less influence of atmospheric turbulence on the SOP of PCEAVB.It can be also found that PCEAVB is less effect ed by the non-Kolmogorov atmospheric turbulence with strong anisotropy and the beams will evolve more slo wly.