This paper provides a comparison of global path planning method in single string by using pulled and pushed SOFM (Self-Organizing Feature Map) which is a method among a number of neural network. The self-organizing feature map uses a randomized small valued initial-weight-vectors, selects the neuron whose weight vector best matches input as the winning neuron, and trains the weight vectors such that neurons within the activity bubble are move toward the input vector. On the other hand, the modified SOFM method in this research uses a predetermined initial weight vectors of the one dimensional string, gives the systematic input vector whose position best matches obstacles, and trains the weight vectors such that neurons within the activity bubble are move toward or reverse the input vector, by rising a pulled- or a pushed-SOFM. According to simulation results one can conclude that the modified neural networks in single string are useful tool for the global path planning problem of a mobile robot. In comparison of the number of iteration for converging to the solution the pushed-SOFM is more useful than the pulled-SOFM in global path planning for mobile robot.