How to suppress the background noise and also recover signals is a widely-concerned and long standing problem in the field of seismic data processing. Effective seismic denoising methods can significantly enhance the quality of seismic data and its signal-to-noise ratio (SNR). Recently, deep-learning-based denoising methods have developed rapidly and achieved more remarkable results than traditional methods. To follow this promising trend and further reinforce the denoising performance, we propose a progressive denoising network (PDN) for land prestack seismic data and apply it to suppress the random noise and surface waves. This proposed PDN contains a feature extraction sub-network and a layer-by-layer denoising sub-network. With the cooperation of the two PDN achieves the layer-by-layer accurate separation of signals and noise according to the difference of low and high features extracted by applying continuous convolution operations. In addition, we utilize both synthetic and real seismic data to construct a rich training dataset with high authenticity and then adopt random-patch-based method to fed the network. The denoising result of synthetic example indicates the excellent attenuation performance of random noise by using PDN. In real example, PDN removes the random noise and surface waves from real land prestack seismic data simultaneously. Furthermore, compared with two existing deep-learning-based denoising methods, PDN has a stronger ability to recover weak reflections.