DNA computing is a new computing method that has high efficiency in solving large-scale nonlinear and Non-deterministic Polynomial complete problems. The design of DNA sequences is an important step in DNA computing, and the quality of the DNA sequences directly affects the accuracy of DNA computing results. Efficiently designing high-quality DNA sequences is currently a significant challenge. In order to improve the efficiency of DNA sequence design, a sparrow evolutionary search algorithm (SESA) is proposed by us. It inherits the fast convergence of the sparrow search algorithm and avoids the situation that the sparrow search algorithm is prone to fall into a local optimum, which greatly improves the search performance of the algorithm on discrete numerical problems. In order to improve the quality of DNA sequence, a new constraint, multiple GC constraint, has been proposed in this paper. Simulated experiments in NUPACK show that this constraint can greatly improve the quality of the DNA sequences designed by us. Compared with previous results, our DNA sequences have better stability.