The interaction potential energies of water-water and water-methane in structure-I unit cell of methane hydrate are calculated from 2.1 to 8.0A using density functional theory (DFT) B3LYP/TZVP. The curves of potential energies are corrected for basis set superposition error (BSSE) and dispersion interaction using a 4-term L-J (4,6-8,12) correction equation, which is derived from CCSD(T)/cc-pVTZ calculations of water-water and water-methane molecular pairs, using least squares curve-fitting. The methane hydrate unit cell is a regular water dodecahedron cell consisting of 20 water molecules with a methane molecule in the center. The geometries of water and methane are optimized at CCSD(T)/cc-pVTZ level. The BSSE-corrections are calculated for water-water and water-methane interaction energies as functions of the side length, l, of the dodecahedron cell at B3LYP/TZVP level in the range from 2.1 to 8.0A. The BSSE CP-corrected and dispersion-corrected potential energy surfaces (PES) of water-water and water-methane are useful for molecular dynamics simulation of gas clathrate-hydrates.