Method of generating functional is developed for the Hubbard model in the case of strong electron correlations. The method is a generalization of the Kadanoff-Baym approach, suggested earlier for conventional fermi-systems, to highly correlated systems. The method deals with equations for electron Green's functions in terms of variational derivatives with respect to fluctuating fields. In the exact equations a mean-field approximation is suggested with taking into account the static fluctuations of charge and spin. Interrelation between this method and the method of composite operators is established. It is shown that a two-poles approximation for the electronic Green's function describes essential features of quasiparticle spectrum and its evolution when changing electron concentration n and on-site Coulomb interaction U . At half-filling ( n  = 1) at U = U c   ~  1.73 W ( W – width of the bare electron band) a phase transition metal-insulator occurs .