Translational and rotational diffusion coefficients and the translation-rotation couplings of the SPC/E water model are investigated in liquid phase by molecular dynamics simulations in the micro-canonical ensemble using a sample of 512 molecules in a cubic box with periodic boundary conditions. The diffusion coefficients and cross-translation-rotation coupling coefficients are computed in the laboratory and/or molecular systems of axes using a Green-Kubo approach. The studied thermodynamic states explore pressures and temperatures in the following ranges: 210–373 K (1 bar); 300–700 K (400, 1000, and 3000 bar), 277 K (1–6000 bar). Translation diffusion is also analyzed using the Einstein approach. The rotational diffusion is also characterized by computing the first and second order correlation times of the OH bond vectors and of the axes of inertia of the water molecule.