Large-scale and long-time molecular-dynamics simulations are used to investigate the temperature dependences of elastic properties for amorphous SiO2. The elastic moduli increase in a temperature range up to 1600 K and decrease thereafter. The anomalous behaviour in elasticity is explained by analysing the changes of atomic-scale structure with respect to increment of temperature. The mechanism originates predominantly from distortion of the SiO4 tetrahedra network in low-temperature ranges. At an elevated temperature range, thermal-induced Si-O bond stretching dominates the process and leads to normal temperature dependence of elastic properties.