The amplitude of the marine controlled source electromagnetic (CSEM) signal decays dramatically with the augment of offset. The signal is easily contaminated by surrounding noise when the transmitter-receiver offset is large. Denoising is crucial for marine CSEM data processing and interpretation. Nowadays, most denoising methods focus on suppressing the noise influences for a single component. The inherent relations among different electromagnetic (EM) components are neglected. Besides, some weak signals are removed mistakenly to get a better denoising effect. In this paper, a new denoising method is proposed based on a jointly sparse model and dictionary learning, which utilizes the correlations among multi-components of marine CSEM data. Synthetic experiments prove that it can not only effectively remove noise, but also successfully protect weak signals. Field data application further validates the effectiveness of the proposed method.