We have developed high-pressure NMR technique with an Indenter Cell using NiCrAl alloy. It was designed to set easily into a conventional dilution fridge and/or high field magnet. We have succeeded in ⁷Li-NMR measurement of a heavy fermion spinel LiV₂O₄ in T-range between 60 mK and 30 K under pressure up to 4.7 GPa. At ambient pressure, 1/T₁ shows a broad maximum around 50 K and is proportional to the temperature below 6 K. This is quite similar to the relaxation behavior in f-electron HF systems. However, 1/T₁T becomes larger with applying higher pressure below 10 K and does not obey T₁T = constant relation down to 1 K. Knight shift K, meanwhile, is independent of pressure above 2 GPa, indicating that the uniform component of susceptibility χ(0) does not change under high pressure. Some antiferromagnetic fluctuations with wave vector q ≠ 0 dominate relaxation rate in LiV₂O₄ near the boundary of the pressure induced insulating phase.