Dynamics of water and poly(N-isopropylacrylamide) (PNIPA) in concentrated aqueous solutions, where the majority of water molecules are attached to polymer chains, has been investigated with use of incoherent quasi-elastic neutron scattering (QENS) and dynamic light scattering (DLS) measurements as functions of temperature, T, and hydrostatic pressure, P. It was observed by QENS that the self-diffusion coefficient, D-water, of water in PNIPA/H2O Solutions increased by P at temperatures below the lower critical solution temperature (LCST) of PNIPA aqueous solutions. However, above the LCST, D-water, decreased by P, as is often reported in non-hydrogen bonding solutions. In isobaric beating runs, therefore, the jump in D-water at LCST decreased with increasing pressure. On the other hand, the mean-square displacement, < u(2)>, of the local vibrational motion of PNIPA in PNIPA/D2O solutions, where the incoherent scattering signal of PNIPA was predominantly observed, was reduced due to the aggregation behavior of PNIPA by pressurizing, which was also confirmed by using DLS. The jump in < u(2)> at the LCST became gradual by pressurizing, which was consistent with the changes of the dynamics of water obtained in PNIPA/H2O solutions.