In solar radio observation, it is inevitable to be disturbed by noise, and the solar radio spectrum is affected. The solar radio spectrum with good quality can provide useful information in analyzing solar activities and improve the accuracy of automatic detection and classification of solar radio bursts. A noise reduction method for solar radio spectrum based on improved guided filter and morphological cascade is proposed in this paper. Firstly, the background noise of solar radio spectrum is subtracted, and the cross-fringe interference caused by channel effect is reduced. Secondly, the improved guided filtering is used to keep the edge of the solar radio burst as far as possible when filtering the burst region of the spectrum. Finally, more noise from other external factors is removed by morphological operation. The experimental results show that the proposed method is effective in removing noise from solar radio spectrum.