Abstract DNA computing was proposed for solving a class of intractable computational problems, of whichthe computing time will grow exponentially with the problem size. Up to now. many achievements have been made to improve its performance and increase its reliability. It has been shownmany times that the surface-based DNA computing technique has very low error rate, but the technique has not been widely used in the DNA computing algorithms design. In this paper, a surface-based DNA computing algorithm for minimal vertex cover problem, a problem well-known for its exponential difficulty, is introduced. This work provides further evidence for the ability of surface-based DNA computing in solving NP-complete problems.