This paper deals with a neural network guidance law based on pursuit-evasion games, and performance enhancing methods for the neural network guidance. Two-dimensional pursuit-evasion games solved by using the gradient method are considered. The neural network guidance law in this work employs the range, range rate, line-of-sight rate, and heading error as its input variables. An additional network training method and a hybrid guidance method are proposed for the sake of the interception performance enhancement. Numerical simulations are accompanied for the verification of the neural network guidance law, and validation of the performance enhancement achieved by the proposed methods. Moreover, all proposed guidance laws are compared with proportional navigation.