The solution of brachistochrone problem turned out the form of a cycloid but correct angle values of bead can be obtained from the table form of inverse relations for the complicated nonlinear equations. To enhance the accuracy, this paper employs the neural network to represent the inverse relation of the complicated nonlinear equations. The accurate minimum-time control is possible with the interpolation property of the neural network. For various final target points, we have found that the proposed method is superior to the conventional ones through the computer simulations.