To produce the structural steel plate excellent in damping and toughness without containing an expensive alloy metal and with using a conventional production facility by subjecting a ferritic single phase damping alloy to controlled rolling at a specified finish temp., heating at a specified temp. for a specified time and cooling.

An Al-Si-Fe damping alloy has a composition consisting of, by weight, 2.2-2.8% Al, 0.4-0.6% Si, ≤1.5% Cu, ≤1% Ni, ≤1% Cr, ≤0.01% C, ≤0.01% N, ≤0.1% Mn, ≤0.01% P and the balance essentially Fe. This damping alloy is subjected to controlled rolling at a finish temp. of 600-900°C. The damping alloy is heated/cooled under a condition of a temp. T (K) and a time (t) (hr) in the range a tempering parameter P satisfying a formula. There is no need to intentionally incorporate an expensive alloy element of Cu, Ni and Cr, the damping alloy is efficiently produced.