In this paper the propagation of axially symmetric compression wave in an infinite transversely isotropic magnetoelectroelastic cylinder is presented. Following Pan(2002), the general boundary conditions on the surface of the magnetoelectroelastic cylinder are written by a simple vector equation that is similar to the purely elastic counterpart. By assuming the possible form of the solution, the generalized Pochhammer frequency equations are presented and the corresponding phase velocity curves in some range are given. Numerical examples are also presented to show phase velocity curves under the first 4 kinds of boundary conditions. Other boundary conditions can be studied under farther research.