This paper investigates an application of feedforward neural networks (FNN) to a tracking-control technique in order to render it model-free. The controller, proposed elsewhere by an author of this paper, is based on the Newton-Raphson fluid-flow dynamics for matching a system's predicted output to a target-reference signal. Most of the extant results require that the predictor be based on a knowledge of the input-output system's model. In order to overcome this limitation, we construct the predictor using an FNN slated to provide adequate approximations to future outputs. We test by simulation the efficacy of the resulting controller in a model-free environment, and compare it to results obtained from a model-based approach. The respective results are not far apart, suggesting that the FNN-based model-free controller may have a scope in future applications.