Pressure-induced hydrogen bond symmetrization of InOOH as well as its effects on the elastic properties is investigated by first-principles simulation. The results indicate that the hydrogen bond in InOOH symmetrized at about 18 GPa, resulting in the pressure derivative of the b/c axial ratio changing from negative to positive. While the a/c axial ratio increases with the increasing pressure over a range of 0-40 GPa, its pressure derivative does not change significantly across the hydrogen bond symmetrization. In the text, A-InOOH denotes the asymmetric hydrogen bond phase and S-InOOH refers to the symmetric hydrogen bond phase. The compressional and off-diagonal elastic constants, bulk modulus B, Poisson's ratio , B/G (G represents shear modulus) and longitudinal wave velocity VP increase with the increasing pressure in both A-InOOH and S-InOOH. These properties of A-InOOH are significantly smaller than those of S-InOOH, and therefore they increase abnormally during the hydrogen bond symmetrization, such as a 20%-40% increase of the bulk modulus. Shear modulus G and Young's modulus E increase with the increasing pressure in A-InOOH, but decrease with the increasing pressure in S-InOOH, implying that hydrogen bond symmetrization would change their pressure evolution trends obviously. Shear elastic constant C44 and shear wave velocity VS decrease with the increasing pressure in both A-InOOH and S-InOOH, and more quickly in the latter, indicating that the structure change of hydrogen bond would change their pressure evolution rates. The Young's moduli along the100,010 and001 directions increase with the increasing pressure in A-InOOH, while decrease with the increasing pressure in S-InOOH, and those along the110,110,110 and110 directions always increase with the increasing pressure over a range of 0-40 GPa. The anisotropy and toughness of InOOH increase with the increasing pressure in both A-InOOH and S-InOOH, and the hydrogen bond symmetrization results in abnormal increase. In the materials containing hydrogen bonds, the effects of hydrogen bond symmetrization on different compressional elastic constants depend on the hydrogen bond projection on corresponding axes:the bigger the projection, the more significant the effect is. InOOH has an obviously smaller bulk modulus than -AlOOH. The dominant reason is that the In3+ radius (0.81 , 1 =0.1 nm) is larger than Al3+ radius (0.50 ), resulting in the weaker interaction between In3+ and O2- than that between Al3+ and O2-. In addition, InOOH has more vacancies than -AlOOH. Combining with previous investigations on other rutile-distorted MOOH (M= Al, Ga, Fe, Cr), we can infer that the axial ratios, elastic properties and wave velocities of all MOOH materials have similar pressure evolutions to those of InOOH, and the hydrogen bond symmetrization has similar effects on the properties of MOOH.