To improve the naturalness of reconstructed speech, nonlinear speech models are paid more and more attention in recent years. A nonlinear speech model for speech synthesis based on Support Vector Machine (SVM) is presented firstly. After speech signal is embedded into phase space, nonlinear map in the model is obtained with support vector regression. It is shown in the experiments that for some pieces of speech, not only can speech be perfectly reconstructed by the system, but also jitter and shimmer in the original signal is preserved. However, the output of the system is quite different from the original one for other pieces. The reason is that the sub-bands with different frequency in the original signal can not be perfectly described by a SVM-based autoregressive model trained with one set of training parameters. Consequently, a multi-band model is then proposed. After the original speech is decomposed into several bands through wavelet packet decomposition, a nonlinear dynamical model based on SVM is constructed for each sub-band signal. It is shown in the experiments that the stability of such system is improved.