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Abstract This paper is concerned with homogenization of p-Laplace equations with rapidly oscillating periodic coefficients. The main difficulty of this work is due to the nonlinear structure in this field concerning p-Laplace equations itself. Utilizing the layer and co-layer type estimates as well as homogenization techniques, we establish the desired error estimates. As a consequence, we obtain the rates of convergence for solutions in W01,p $W_{0}^{1,p}$ as well as Lp $L^{p}$. Meanwhile, our convergence rate results do not involve the higher derivatives any more. This may be viewed as rather surprising. The novelty of this work is that it seems to find a new analysis method in quantitative homogenization.