In DNA based computation and DNA nanotechnology, the design of good DNA sequences has turned out to be an essential problem and one of the most practical and important research topics. Basically, the DNA sequence design problem is a multi-objective problem, and it can be evaluated using four objective functions, namely, H _measure , similarity, continuity, andhairpin. There are several ways to solve a multi-objective problem, such as value function method, weighted sum method, and using evolutionary algorithms. However, in this paper, common method has been used, namely weighted sum method to convert DNA sequence design problem into single objective problem. Binary particle swarm optimization (BinPSO) is proposed to minimize the objective in the problem, subjected to two constraints: melting temperature and GC _content . Based on experiments and researches done, 20 particles are used in the implementation of the optimization process, where the average values and the standard deviation for 100 runs are shown along with comparison to other existing methods. The results obtained verified that BinPSO can suitably solve DNA sequence design problem using the proposed method and model, comparatively better than other approaches.