Noise attenuation has been a long-standing but still active topic in seismic data processing. The deep convolutional neural networks (CNNs) have been recently adopted to remove the learned random noise from noisy seismic data, but it is still difficult to improve the generalization ability of learned denoisers due to the limited diversity of training data sets. In this letter, we investigate an end-to-end deep denoising CNNs (DCNNs) with a novel data generation method involving multidimensional geological structure features for seismic denoising. To learn an optimized network denoiser, seismic amplitude data are extracted from 3-D synthetic seismic data along three directions (i.e., two spatial directions and one temporal direction) to prepare a training data set. Compared with using seismic data from only a certain single direction to generate all training samples, this strategy enables DCNNs to learn abundant geological structural information from three directions, and helps DCNNs have a better performance on noise reduction. Another 3-D synthetic seismic data and 3-D real land data examples with plentiful faults and fluvial channels are used to illustrate that the optimized network denoiser can be directly extended to attenuate random noise. The denoising results demonstrate that DCNNs learned from the multidimensional geological structures can accomplish the self-adaptive random noise attenuation, and meanwhile preserve spatial geological structures.