A parallel algorithm for solving the planarization problem using a gradient ascent learning of Hopfield network is presented. This algorithm which is designed to embed a graph on a plane, uses the Hopfield neural network to get a near-maximal planar subgraph, and increase the energy by modifying weights in a gradient ascent direction to help the network escape from the state of the near-maximal planar subgraph to the state of the maximal planar subgraph or better one. The proposed algorithm is verified by a large number of simulation runs and compared with other parallel algorithms for the planarization problem. The experimental results show that the proposed algorithm can generate as good as or better solutions than the other existing parallel algorithm for the planarization problem.