The elastic membranes with different surface stiffness were fabricated via spin-coating followed by the laser ablation. The as-fabricated elastic membrane exhibited superhydrophobicity with a rough microstructure. The droplet impacting experiment on the cold elastic superhydrophobic membrane was conducted, and the influence of surface stiffness and impacting speed on the droplet impacting process were investigated. It was found that the elastic superhydrophobic membrane exhibits a robust anti-icing performance compared with the elastic hydrophobic membrane. A lower surface stiffness corresponds to a larger deformation degree of the elastic membrane and to a smaller maximum droplet spreading diameter. Moreover, the contact time decreases with the increase of impacting speed as for the same stiffness of the cold elastic superhydrophobic membrane. The underlying mechanism of the cold elastic membrane with low ice adhesion may be due to the face that the deformation of the superhydrophobic membrane provides an elastic force for the droplet to detach from the surface and thus reduce the heat transfer between the droplet and the surface.