This paper proposes a gradient ascent learning algorithm of the Hopfield neural networks for graph planarization. This learning 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 applied to several benchmark graphs up to 150 vertices and 1064 edges. The performance of the proposed algorithm is compared with that of Takefuji/Lee’s method. Simulation results show that the proposed algorithm is much better than Takefuji/Lee’s method in terms of the solution quality for every tested graphs.