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The broadband ferromagnetic resonance study on both the single crystalline and polycrystalline Fe wires were performed using the rectifying effect. The effective Gilbert damping in the polycrystalline Fe wire was about three times larger than that in the single crystalline wire. This is attributed to the enhancement of the energy dissipation due to the incoherent rotation of the magnetization at the grains and grain boundaries in the polycrystalline wire. The difference between the experimental data and analytical calculation can be explained by the strong magnetic shape anisotropy that overcomes the external static magnetic field and forces the magnetization to be directed along the wire axis.