Abstarct: Noises in seismic data are divided into two general categories, coherent noises and non-coherent noises (random). Coherent noises from one trace to another trace have a definite trend, while random noises are uncorrelated and do not have a definite trend from one trace to another, and occur as random oscillations in all the length and frequency are emitted along with the original signal. Random noise attenuation in seismic data requires employing leading edge methods to attain reliable denoised data. Efficient noise removal, effective signal preservation and recovery, reasonable processing time with the minimum signal distortion and seismic event deterioration are properties of a desired noise suppression algorithm. There are various noise attenuation methods available that more or less contains these properties. The tensor optimal shrinkage singular value decomposition (T-OSSVD) method contains all the aforementioned properties and is supposed to be an efficient noise suppression method. It faces with problem in effective extraction of low rank of the signal and therefore efficient noise elimination, specifically in high noise contaminated seismic data from subsurface complex structures disturbing the wave propagation in the media. Here we improve performance of the T-OSSVD method by employing continuous wavelet transform (CWT) in the algorithm for extracting the singular values and new method for singular values shrinkage. The noise removal procedure could be performed more efficiently in the wavelet domain with the optimized coefficient compared to the T-OSSVD. For performance evaluation of the proposed method, it was applied on two synthetic and a field data examples and results were compared with the competitive random noise suppression methods, the T-OSSVD, the IBTSVT and the BM4D algorithms. Qualitative and quantitative comparison of the proposed method with those of other methods depicted that it could more efficiently eliminate random noise from seismic data.