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This paper is concerned with the existence of periodic solutions for the fully second-order ordinary differential equation u′′(t)=ft,ut,u′t, t∈R, where the nonlinearity f:R3→R is continuous and f(t,x,y) is 2π-periodic in t. Under certain inequality conditions that f(t,x,y) may be superlinear growth on (x,y), an existence result of odd 2π-periodic solutions is obtained via Leray-Schauder fixed point theorem.