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Random noise attenuation is an essential step to improve the signal-to-noise ratio (SNR) of seismic data. Deep learning for seismic data denoising is dominated by supervised methods that require noise-free data as training targets. It is usually time-consuming and laborious to obtain such clean seismic data, and the effectiveness of the noise attenuation is difficult to be guaranteed. Therefore, we propose a novel unsupervised learning method that learns from noisy data. The method is based on two salient features of seismic data: 1) valid signals of adjacent seismic traces that are spatially correlated and 2) random noise that is spatially independent and unpredictable. An end-to-end deep convolutional neural network (CNN) was constructed to solve the denoising task. Adjacent traces of seismic data, which contain similar seismic phases and interface features, were used as the inputs and labels of the training set. The mapping of spatial correlation can be learned by the CNN so that valid signals from raw seismic data are predicted, while random noise is suppressed for unpredictability. Synthetic and field data were applied to the proposed CNN denoising model. The experimental results demonstrate the effectiveness of random noise attenuation while preserving amplitude compared with two commonly used state-of-the-art denoising methods.