The cold atom qubit platform emerges as an attractive choice for the next stage of quantum computation research, where a special family of synthetic analytical pulses has considerably improved the experimental performance of Controlled-PHASE Rydberg blockade gates in recent studies. The success of Controlled-PHASE Rydberg blockade gates triggers the intriguing question of whether the two-qubit Rydberg blockade gate SWAP gate exists. Via investigating the transition linkage structure, we provide a definitive answer to this question and establish the method of fast SWAP Rydberg blockade gates with synthetic continuously modulated driving. These gate protocols use careful analysis to properly generate coherent population transfer and phase accumulation of the wave function in the atom-laser interaction process. They can adapt to finite Rydberg blockade strengths and bear considerable resistance to some major adverse effects such as laser fluctuations. Further examinations reveal that we can anticipate satisfying performances of the method with currently available experimental techniques in relevant research areas.