Seismic field data are usually contaminated by random or complex noise, which seriously affect the quality of seismic data contaminating seismic imaging and seismic interpretation. Improving the signal-to-noise ratio (SNR) of seismic data has always been a key step in seismic data processing. Deep learning approaches have been successfully applied to suppress seismic random noise. The training examples are essential in deep learning methods, especially for the geophysical problems, where the complete training data are not easy to be acquired due to high cost of acquisition. In this work, we propose a natural images pre-trained deep learning method to suppress seismic random noise through insight of the transfer learning. Our network contains pre-trained and post-trained networks: the former is trained by natural images to obtain the preliminary denoising results, while the latter is trained by a small amount of seismic images to fine-tune the denoising effects by semi-supervised learning to enhance the continuity of geological structures. The results of four types of synthetic seismic data and six field data demonstrate that our network has great performance in seismic random noise suppression in terms of both quantitative metrics and intuitive effects.