The phenomenon of droplets impacting elastic surfaces is common in nature and in many engineering applications. It has been shown that droplet impact on an elastic surface drastically reduces droplet contact time and hinders droplet spreading. However, most of the current studies are based on experiments, and the analysis of the influence mechanism of the elastic substrate on the dynamic behavior of droplets is not complete. In addition, the simulations of droplet impact on elastic substrates are mainly focused on 2D elastic films or vibrating rigid substrates, ignoring the effect of 3D elastic substrate deformation on the droplet dynamic behavior. Therefore, in this paper, we propose to model the droplet impact on a 3D hydrophobic elastic substrate using the molecular dynamics method. We find that droplet pancake rebound can substantially reduce the droplet contact time. Moreover, we record the conditions required for the pancake rebound of the droplet. Furthermore, we investigated the effects of the elastic modulus of the substrate and the initial velocity of the droplet on the droplet contact time, contact area, and spreading factor. This study further elucidates the influence mechanism of the elastic substrate on the dynamic behavior of the droplet and provides theoretical guidance for regulating the dynamic behavior of the droplet in related fields.