In this paper, we have shown that the Boolean Neural Network can be used to solve NP-complete problems. The problem under consideration is the traveling salesman problem. The Boolean Neural Network has been modified to include the iterative procedure for solving combinatorial optimization problems. An architecture that utilizes this modified Boolean Neural Network is proposed for solving this problem. The simulation results have been found to be comparable to the Simulated Annealing algorithm, which is used as a test base. The results show a better variance as compared to Simulated Annealing. The modified Boolean Neural Network implementation involves lesser hardware complexity, good noise immunity and faster circuitry. This is very important in real-time systems and commercial job scheduling applications.