Abstract: This paper studies the Cauchy problem of semi-linear σ-evolution equations with structural damping, and the （L^m∩L²）-L²and L²-L² estimates of the solutions of the corresponding linear problems are established by Fourier analysis. Employing the global iJP3terative method and assuming small initial data, when the nonlinear term exponent p and the spatial dimension n meet certain conditions, the global existence and uniqueness of the solutions are proved and the decay estimates are obtained.