A neural network (NN)-based cascade control system is developed, in which the primary proportional-integral-derivative (PID) controller is constructed by NN. A new entropy-based measure, named the centred error entropy (CEE) index, which is a weighted combination of the error cross-correntropy (ECC) criterion and the error entropy criterion (EEC), is proposed to tune the NN-PID controller. The purpose of introducing CEE in controller design is to ensure that the uncertainty in the tracking error is minimised and also the peak value of the error probability density function being controlled toward zero. The NN-controller design based on this new performance function is developed and the convergent conditions are investigated using a linearisation technique. During the control process, the CEE index is estimated by a Gaussian kernel function. Adaptive rules are developed to update the kernel size in order to achieve more accurate estimation of the CEE index. This NN cascade control approach is applied to superheated steam temperature control of a simulated power plant system, from which the effectiveness and strength of the proposed strategy are discussed by comparison with NN-PID controllers tuned with EEC and ECC criterions.