The new hexagonal aluminous phase, named the NAL phase, is expected to be stable at depths of <1200 km in subducted slabs and believed to constitute 10~30 wt% of subducted mid-ocean ridge basalt together with the CaFe2O4-type aluminous phase. Here elasticity of the single-crystal NAL phase is investigated using Brillouin light scattering coupled with diamond anvil cells up to 20 GPa at room temperature. Analysis of the results shows that the substitution of iron lowers the shear modulus of the NAL phase by ~5% (~6 GPa) but does not significantly affect the adiabatic bulk modulus. The NAL phase exhibits high-velocity anisotropies with AVP = 14.7% and AVS = 15.12% for the Fe-bearing phase at ambient conditions. The high AVS of the NAL phase mainly results from the high anisotropy of the faster VS1 (13.9~15.8%), while the slower VS2 appears almost isotropic (0.1~2.8%) at ambient and high pressures. The AVP and AVS of the NAL phase decrease with increasing pressure but still have large values with AVP = 11.4% and AVS = 14.12% for the Fe-bearing sample at 20.4 GPa. The extrapolated AVP and AVS of the Fe-free and Fe-bearing NAL phases at 40 GPa are larger than those of bridgmanite at the same pressure. Together with its spin transition of iron and structural transition to the CF phase, the presence of the NAL phase with high-velocity anisotropies may contribute to the observed seismic anisotropy around subducted slabs in the uppermost lower mantle.