The volume's exponential explosion problem has been the critical factor that constraints the development of the DNA computing. For the objective to decrease the DNA volume complex of the vertex cover problem which is a famous NP-complete problem, a new DNA algorithm is advanced. The new algorithm consists of a parallel reducer, a solution generator, a dense parallel searcher, a sparse parallel searcher and a vertex cover searcher. In a computer simulation, the DNA strands of maximum number required is O(√3 ⁿ) on the condition of not varying the time complexity. Besides, this algorithm is highly space-efficient and error-tolerant compared to conventional brute-force searching, and thus can be scaled-up to solve large and hard minimum vertex cover problems.