The linear augmented-Slater-type-orbital (LASTO) method, as one of real-space band theories, is generalized to a spin-polarized Dirac-type density-functional in full potential scheme. Since the Bloch sum of Slater-type orbital can do the Fourier transformation analytically with a conditional convergence, it is not only easily extendable to a full-potential scheme, but also have a high compatibility to a four-component relativistic linear-augmented-plane-wave method. In this paper, the formulation of this full potential Dirac-type LASTO (DLASTO) method is presented in a self-contained manner. By applying it to a typical material for each of the 3d-, 4f-and 5f-electron systems, we discuss some of the cut-off parameters and orbital choices required in the DLASTO calculation and provide guidelines for their settings. In addition, the electronic structure and magnetism for each of these systems will be discussed.