Quasicrystals are a class of materials with long-range order but no translational periodicity. Though many quasicrystals have been discovered, rational design and engineering of quasicrystals remain a great challenge. Herein, we have developed a rational strategy to assemble two-dimensional (2D), dodecagonal quasicrystals from branched DNA nanomotifs. The key of our strategy is to balance the rigidity and flexibility of the motifs, which is controlled by the introduction of interbranch "bridges". By fine-tuning the experimental conditions, we are able to predictably produce either 2D quasicrystals or conventional crystals. This study presents a rational design, prediction and realization of quasicrystal formation.