Random noise attenuation is one of the most essential steps in seismic signal processing. We propose a novel approach to attenuate seismic random noise based on deep convolutional neural network (CNN) in an unsupervised learning manner. First, normalization and patch sampling are required to build training dataset and test dataset from raw noisy data. Instead of using synthetic noise-free data or denoised results via conventional methods as training labels, we adopt only the training set constructed from the raw noisy data as the input and design a robust deep CNN that just relies on the noisy input to learn the hidden features. The cross-entropy is chosen as the error criterion for establishing the cost function, which is minimized by the back-propagation algorithm to obtain the optimized parameters of the network. Then, we can reconstruct all patches of the test dataset via the optimized CNN. After patching processing and inverse normalization, the final denoised result can be obtained from reconstructed patches. Experimental tests on synthetic and real data demonstrate the effectiveness and superiority of the proposed method compared with state-of-the-art denoising methods.