A design of nonlinear-dynamic observer is proposed for determining the states of a nonlinear system. The design method uses a multi-layered feed-forward neural network (MFNN) to approximate the nonlinear Kalman gain. Two different criteria are proposed for the network training. The training is based on a gradient descent algorithm that uses block partial derivatives. Simulation results on Van der Pol＇s equation and the classical inverted pendulum model are presented to validate the usefulness of the scheme.