We performed total energy and electronic structure calculations for the basic ground state properties of Fe using the conventional generalized gradient approximation (GGA) and screened hybrid functionals as the form of the exchange-correlation functional. To that end, we calculated structural (equilibrium lattice constants, bulk moduli, and cohesive energies) and electronic (magnetic moments and densities of states) properties. Both functional calculations gave the correct ground state, the ferromagnetic bcc phase, in which the structural parameters agreed well with experimental results. However, the description of the cohesive energies and magnetic moments at the ground state exhibited different behavior from each other: the unusually small cohesive energy and large magnetic moment were observed in the screened hybrid functional calculations compared to the GGA calculations. The reason for the difference was examined by analyzing the calculated electronic structures.