We study the oscillatory properties of the second order half-linear difference equation Δ(g(t)Δ|u(t)|^(τ-2) Δu(t))+s(t)|Δu(t)|^(τ-2) Δu(t)-h(t)|u(t+1)|^(τ-2) u(t+1)=0, τ>1 (HL) The core ideas of oscillation theory for this equation will be shown to be quite similar to those for the linear equation. Δ(g(t)Δu(t))+s(t)(Δu(t))-h(t)u(t+1)=0. We establish some sufficient conditions related to the oscillatory behavior of the equation(HL). Examples are provided to illustrate the importance of the main results.