In order to clarify whether or not the so-called itinerant-electron model can predict the existence of the ferromagnetism in the narrow d-band or transition metals, an electron gas in a background of a uniform positive charge (single-band model) is considered as a simplest model. On the basis of the interpolation formula for the correlation energy developed by Pines et al., the difference of the energy between the ferromagnetic state and the unpolarized (paramagnetic) state is examined. Contrary to the prevailing view, apparently due to Wigner and Pines, if the dynamical screening for spin-polarized states is correctly taken into consideration, the electron gas then is shown to become ferromagnetic even in the intermediate-density region. The critical value of (m*m)rs [where (m*m) is the ratio of the band effective mass to the free mass of electrons, and rs is the inter-electron spacing in units of the Bohr radius] beyond which the system becomes ferromagnetic lies between 7 and 10. The paramagnetic susceptibility also shows a divergence approximately over the same density range.