Double-helix structures, such as DNA, are formed in nature to realize many unique functions. Inspired by this, researchers are pursuing strategies to design such structures from polymers. A key question is whether the double helix can be formed from the self-folding of a single polymer chain without specific interactions. Here, using Langevin dynamics simulation and theoretical analysis, we find that a stable double-helix phase can be achieved by the self-folding of single semiflexible polymers as a result of the cooperation between local structure and nonlocal attraction. The critical temperature of double-helix formation approximately follows T^{cri}∼ln(k_{θ}) and T^{cri}∼ln(k_{τ}), where k_{θ} and k_{τ} are the polymer bending and torsion stiffness, respectively. Furthermore, the double helix can exhibit major and minor grooves due to symmetric break for better packing. Our results provide a novel guide to the experimental design of the double helix.