Although the self-transport of liquid droplets by a gradient-textured substrate can break away from the energy input, the long distance and even continuous spontaneous motion of droplets will be limited by the length in the surface-gradient direction. This article introduces a novel design with a monolayer graphene-covered multibranch gradient groove surface (GMGGS). The design aims to achieve long-distance, continuous self-transport of a mercury (Hg) droplet by merging with other mercury droplets, and the process is carried out using molecular dynamics (MD) simulation. This method achieves the merging of mercury droplets through the structure of multibranch gradient grooves, and we have observed that the merged mercury droplet can be reaccelerated in the gradient groove. The results demonstrate that droplet merging allows for control over the surface morphology variations of mercury droplets within the gradient groove. This creates a forward pressure difference, which leads to reacceleration of the mercury droplets. In light of this mechanism, the trunk droplet can achieve long-distance continuous self-transport on the GMGGS by continuously merging with branch droplets. These findings will broaden our comprehension of droplet merging and self-transport behavior, offering corresponding theoretical support for the long-distance continuous self-transport of droplets.