The Knight shift K and the nuclear spin-lattice relaxation time T-1 of Li-7 have been measured under high pressure up to 4.74 GPa. 1/T1T becomes larger on applying higher pressure below 10 K and does not obey the T1T = constant relation down to 1 K. Meanwhile, K is independent of pressure above 2 GPa, indicating that the uniform component of the susceptibility does not change under high pressure. These results indicate that some antiferromagnetic fluctuations with wavevector q not equal 0 dominate the relaxation rate in LiV2O4 near the boundary of the pressure induced insulating phase. It is noted that the pressure dependence of T-1 for LiV2O4 is opposite to that of typical Ce HF compounds, such as CeCu5.9Au0.1 and CeCu2Si2. At the highest pressure of 4.74 GPa, we found that 1/T-1 obeys a power law dependence of T-2/3 over the wide T range between 60 mK and 10 K. The spin dynamics under high pressure will be discussed.