For chemical mechanical polishing (CMP) process characteristics of nonlinear, time-varying and not being in-situ measured, this paper proposes a CMP process neural network predictive run-to-run (R2R) controller named NNPR2R. RBF neural network predictive model about CMP is constructed by subractive clustering algorithm and least squares method, thus it solves difficult problem of constructing accurate mathematical model of complicated CMP process and improves the prediction accuracy. control law of model predictive control is obtained by feedback correction and PSO rolling optimization, therefore it solves the problem that derivative-based optimization technology is easy to fall into local optimum and impoves control precision. simulation result illustrate that performance of NNPR2R controller is better than EWMA, process driftsand shiftts is suppressed significantly, product quality variation between different runs is reduced, and root mean squared error for material removal rate (MRR) is brought down substantially.