The operation principle of an axial flux-switching hybrid excitation synchronous machine (AFHESM) is analyzed and its topology structures are proposed in this paper. After some comprehensive analysis of the operation principle to axial flux electrical machine, flux-switching electrical machine and hybrid excitation electrical machine, the operation principle of AFHESM is given. Combined with some typical topological structures of hybrid excitation electrical machine, some possible topological structures are proposed and some comprehensive comparisons are carried out. The analysis results show that the stator-separated AFHESM has some advantages such as less AM turns, less impact on the demagnetization of PM, less magnetic flux-leakage and higher efficiency compared to other topologies.