**Abstract:**
Adleman showed that deoxyribonucleic acid (DNA) strands could be employed towards calculating solutions to an instance of the Hamiltonian path problem (HPP) [3]. Lipton [5] could solve the Satisfiability problem. In this paper, we use that model for developing a new DNA algorithm to solve minimum independent dominating set problem (MIDSP). In spite of the NP-hardness of minimum independent dominating set problem (MIDSP) our DNA procedures is done in a polynomial time.

**Keywords:**
DNA computing, minimum independent dominating set problem.