The behavior of hydrate formation in porous sediment has been widely studied because of its importance in the investigation of reservoirs and in the drilling of natural gas hydrate. However, it is difficult to understand the hydrate nucleation and growth mechanism on the surface and in the nanopores of porous media by experimental and numerical simulation methods. In this work, molecular dynamics simulations of the nucleation and growth of CH4 hydrate in the presence of the surface and nanopores of clay are carried out. The molecular configurations and microstructure properties are analyzed for systems containing one H2O hydrate layer (System A), three H2O hydrate layers (System B), and six H2O hydrate layers (System C) in both clay and the bulk solution. It is found that hydrate formation is more complex in porous media than in the pure bulk solution and that there is cooperativity between hydrate growth and molecular diffusion in clay nanopores. The hydroxylated edge sites of the clay surface could serve as a source of CH4 molecules to facilitate hydrate nucleation. The diffusion velocity of molecules is influenced by the growth of the hydrate that forms a block in the throats of the clay nanopore. Comparing hydrate growth in different clay pore sizes reveals that the pore size plays an important role in hydrate growth and molecular diffusion in clay. This simulation study provides the microscopic mechanism of hydrate nucleation and growth in porous media, which can be favorable for the investigation of the formation of natural gas hydrate in sediments.