A seismic signal blind denoising algorithm is proposed based on W-weighted nuclear norm minimization. The noise level of seismic signals is estimated by principal component analysis and the denoising is realized by weighted nuclear norm minimization (WNNM). In denoising, the shrinkage degree of singular values of a matrix is controlled by weight assignment, and the performances of the algorithm is improved. Three kinds of seismic signals are denoised, respectively. The performance is compared with double tree complex wavelet transform, curvelet transform and the WNNM algorithm. The research results show that the proposed algorithm can effectively remove the noises contained in seismic signals when the noise level is unknown. Moreover, the denoising effect is superior to those of the traditional denoising algorithms.