For the fabrication of particular nanostructures, Stranski-Krastanov (SK) growth mode driven by strain is most widely used. Meanwhile, another technique that is used to form the complex nanostructures is the droplet epitaxy technique, which is based on the deposition of group III element nanoscale droplets onto substrate and followed by the reaction with group V element for crystallization into III-V compound nanostructures. Droplet epitaxy technique is simple and flexible, and it does not require additional complicated processing and has potential to develop various quantum nanostructures. It, unlike standard MBE growth, exploits the sequential supply of group-III and group-V elements to form quantum nanostructures. Quantum rings are a special class of quantum-confinement structure that can be fabricated by the droplet epitaxy technique and have attracted wide attention due to the Aharonov-Bohm effect, which is specific to the topology of a ring. In this paper, GaAs/GaAs (001) concentric quantum double rings (CQDRs) are prepared by droplet epitaxy technique at different Ga droplet deposition rates in monolayer per second (ML/S). The 2 μm × 2 μm atomic force microscope images are obtained to show the morphologies of CQDRs. We study the effects of Ga droplet deposition rates (0.09 ML/s, 0.154 ML/s, 0.25 ML/s, 0.43 ML/s) on CQDRs. The results show that with the increase of Ga droplet deposition rate, the density of CQDRs increases and the radius of inner ring and the radius of outer ring decrease. According to the nucleation theory, through the relationship between the maximum cluster density and the Ga droplet deposition rate, the critical number of atom nucleations is found to be 5, which suggests that the stable Ga atom crystal nucleus should contain at least 5 Ga atoms in the process of forming Ga droplet, and a nucleation state transformation diagram is drawn in order to obtain an insight into the process of forming Ga droplet according to the nucleation theory and fitting results. The research results could be instructive for preparing the GaAs concentric quantum double rings that the density can be controlled by droplet epitaxy.