We investigate the anomalous structure and hydrogen bond network of water molecules confined inside a silica nanopore (MCM-41 type). In addition to geometric data, we use proton NMR chemical shifts as a measure for the strength of the H-bonding network. We compute the 1H NMR shifts of confined water based on a first principle approach in the framework of density functional perturbation theory under periodic boundary conditions. The hydrophilic character of the silica is well manifested in the water density profile. Our calculations illustrate both the modifications of the 1H NMR chemical shifts of the water with respect to bulk water and a considerable slowing down of water diffusion. In the vicinity of silanols, weakly hydrogen bonded liquid water is observed, while at the center region of the pore, the hydrogen bonding network is enhanced with respect to bulk water.