It is known that the Brownian motion on the Sierpinski carpet has sub-Gaussian behavior (it is also called anomalous diffusion), and so we can not develop the upper gradient based analysis on the Sierpinski carpet. In this talk, I will give a construction of a ``canonical'' p-energy (formally written as $\int |\nabla f(x)|^p dx$) on the Sierpinski carpet as a scaling limit of discrete energies on approximating graphs. I also plan to describe associated energy measures.