A neural network controller is described for controlling unknown, linear, discrete-time CARMA systems with single-input single-output. A linear two-layered neural network is used to model the inverse dynamics of the unknown plant on-line; it is learned by the delta rule, in which the difference between the actual control input to the plant, which is generated from the neural controller, and the input estimated from the inverse-dynamics model by using an actual plant output is minimized. A similar neural network is also used to estimate the unknown noise sequence so that the proposed neural network controller can treat a noisy output, where the regular dynamics are modelled on-line by using the actual plant output. Some simulation examples are finally presented to illustrate the features of the present neural controller.