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This note studies the existence of positive homoclinic orbits of the second orde r equation-u″+α(x)u=β(x)uq+γ(x)up, x∈R,where 1＜q＜p.Assume that the coefficient functions α(x),β(x) and γ (x) are asymptotically periodic and satisfy0＜a≤α(x), 0＜γ(x)≤B, -M≤β(x)≤M.A positive omoclinic orbit of the equation is obtained by means of variational methods.