A state prediction scheme is proposed for discrete time nonlinear dynamic systems with non-Gaussian disturbance and observation noises. This scheme is based upon quantization, multiple hypothesis testing, and dynamic programming. Dynamic models of the proposed scheme are as general as dynamic models of particle predictors, whereas the nonlinear models of the extended Kalman (EK) predictor are linear with respect to the disturbance and observation noises. The performance of the proposed scheme is compared with both the EK predictor and sampling importance resampling ( SIR) particle predictor. Monte Carlo simulations have shown that the performances of the proposed scheme, EK predictor, and SIR particle predictor are all model-dependent, that is, one performs better than the others for a given example. Some examples, for which the proposed scheme performs better than the others do, are also given in the paper.