Spontaneous cortical activity -- the ongoing cortical activities in absence of intentional sensory input -- is considered to play a vital role in many aspects of both normal brain functions and mental dysfunctions. We present a centered Gaussian-binary Deep Boltzmann Machine (GDBM) for modeling the activity in early cortical visual areas and relate the random sampling in GDBMs to the spontaneous cortical activity. After training the proposed model on natural image patches, we show that the samples collected from the model's probability distribution encompass similar activity patterns as found in the spontaneous activity. Specifically, filters having the same orientation preference tend to be active together during random sampling. Our work demonstrates the centered GDBM is a meaningful model approach for basic receptive field properties and the emergence of spontaneous activity patterns in early cortical visual areas. Besides, we show empirically that centered GDBMs do not suffer from the difficulties during training as GDBMs do and can be properly trained without the layer-wise pretraining.