The spin-1/2 anisotropic Heisenberg ferromagnet with a transverse field is studied by the use of a new method, which combines the two-spin cluster expansion with the perturbation theory. The phase diagrams in which the transition temperature is shown as a function of the transverse field as well as the exchange anisotropic parameter are obtained for a two-dimensional square lattice and a three-dimensional simple cubic lattice. The results can be compared with that of mean field renormalization group (MFRG) and variational-cumulant expansion (VCE).