We investigated the magnetoelastic properties of the quasi-one-dimensional spin-12 frustrated magnet LiCuVO4. Longitudinal-magnetostriction experiments were performed at 1.5 K in high magnetic fields of up to 60 T applied along the b axis, i.e., the spin-chain direction. The magnetostriction data qualitatively resemble the magnetization results, and saturate at Hsat≈54 T, with a relative change in sample length of ΔL/L≈1.8×10-4. Remarkably, both the magnetostriction and the magnetization evolve gradually between Hc3≈48 T and Hsat, indicating that the two quantities consistently detect the spin-nematic phase just below the saturation. Numerical analyses for a weakly coupled spin-chain model reveal that the observed magnetostriction can overall be understood within an exchange-striction mechanism. Small deviations found may indicate nontrivial changes in local correlations associated with the field-induced phase transitions.