This research is an introduction to density functional theory (DFT), which has been designed for Floating Spherical Gaussian Orbital (FSGO) method for the first time. Our principal objective is to apply a combination of energy functionals to the FSGO densities. The functionals used are separated into exchange and correlation parts. For the exchange part the Becke exchange that includes gradient correction is used. The correlation part has been carried out using Lee, Yang and Parr gradient-corrected functional. Three goals are investigated in this research. Is it possible to apply DFT in the FSGO procedure to obtain the electronic structure of chemical species? Second, is it a stable condition, from the variational point of view, during optimization of exponents and coefficients of each Gaussian? Thirdly, when the two above questions are encouraging, are the results consistent with other results in the literature? In this research we are looking for acceptable answers to the above questions.