Neural networks have been known as flexible nonlinear black-box models and have attracted much interest in control community. This paper introduces a new neural-network based prediction model for control of nonlinear systems. Distinctive features of the new model to the conventional neural-network based ones are that it has not only meaningful interpretation on part of its parameters but also is linear for the input variables. The former feature makes the parameter estimation easier and the latter allows deriving a nonlinear controller directly from the identified prediction model. The modeling and the parameter estimation are described in detail. The usefulness of the new model is demonstrated by applying it to control of two simulated nonlinear black-box systems.