A general temperature calculation method of axisymmetric multilayer cylinder was deduced according to the axisymmetric heat conduction of cylinder. Four types of combined boundary conditions were summarized, and temperature computational formulas of axisymmetrical monolayer cylinder were formed under each type. The intermediate interface temperatures and radial stresses of axisymmetrical multilayer cylinder satisfy tridiagonal linear system of eouations, which can be solved with pursuit method. The calculation method is applied universally. Meanwhile, the corresponding calculating program was developed.