This paper presents an iterative learning algorithm for functional approximation, with applications to the robot kinematics problems. Various approaches have been proposed in the literature to approximate the kinematic models of robots. However, most of them assume that either the kinematic parameters or the kinematic structures of the robots are known. Neural network (NN) has been known for its inherent functional approximation capability and can be used to approximate the models when the structures of the robots are unknown. Most of these NN methods are formulated as gradient-based learning algorithms and there is no theoretical analysis to ensure convergence. Our proposed method in this paper does not require any computation of the gradient of the cost function or the inverse matrix. The convergence of the algorithm is guaranteed by theoretical analysis. The performance of the algorithm is illustrated by using a radial basis function (RBF) neural network to approximate the kinematic models of two different robots.