Zermelo's navigation problem is that the ship reaches a particular target point in the minimum-time when it travels with a constant speed in a region of strong currents and its heading angle is the control variable. Its approximate solution for the minimum-time control may be found using the calculus of variation. However, the accuracy of its approximate solution is low since the solution is based on graph or table form from a complicated nonlinear equations. To improve the accuracy, we use a neural network. Through the computer simulation study we have found that the proposed method is superior to the conventional ones.