This paper proposes a new speech bandwidth expansion method, which uses Deep Neural Networks (DNNs) to build high-order eigenspaces between the low frequency components and the high frequency components of the speech signal. A four-layer DNN is trained layer-by-layer from a cascade of Neural Networks (NNs) and two Gaussian-Bernoulli Restricted Boltzmann Machines (GBRBMs). The GBRBMs are adopted to model the distribution of spectral envelopes of the low frequency and the high frequency respectively. The NNs are used to model the joint distribution of hidden variables extracted from the two GBRBMs. The proposed method takes advantage of the strong modeling ability of GBRBMs in modeling the distribution of the spectral envelopes. And both the objective and subjective test results show that the proposed method outperforms the conventional GMM based method.