Random noise attenuation is a critical step in seismic data processing. Since the distribution of field noise is complex and unknown, this poses a challenge to noise attenuation methods where the default noise distribution is known, such as a Gaussian distribution. To address this issue, we propose a method called seismic random noise Gaussianization framework (SRNGF) to attenuate random noise with unknown distribution. Specifically, SRNGF couples the Gaussianization subproblem and Gaussian denoising subproblem based on the plug-and-play (PaP) framework. The Gaussianization submodule with learnable parameters maps seismic data with the noise of unknown distribution to the one corrupted by Gaussian noise. The learnable parameters can be updated through unsupervised online training according to the noise of the unknown distribution on a single field data. The Gaussian denoising submodule, which can be replaced by seismic denoiser, aims only for Gaussian noise removal, making SRNGF incorporate the denoiser prior to seismic data. Thus, we incorporate different kinds of seismic nondeep/deep learning (DL) denoisers into SRNGF and give their corresponding implementations of SRNGF. Experiments on noise with unknown distribution qualitatively and quantitatively validate the superiority of SRNGF. SRNGF improves the results of non-DL/DL seismic denoiser by a large margin.