Self-organizing map network （SOM） is a classic unsupervised learning method with self-organizing and online learning functions. Due to its simplicity and practicality， SOM variants have been emerging to adapt to various problems. However， these work basically adopts deterministic neurons to build networks， ignoring the uncertainty information implicit in the data itself. This results in a lack of interpretability reflected by confidence in the results of these models， implying that the uncertainty characterization ability of SOM neurons is insufficient. This article proposes a new variant of SOM， called the Gaussian neuron SOM network （GNSOM）. Its neuron nodes are no longer deterministic， but modeled as Gaussian neurons with Gaussian distribution. Thus， SOM is equipped with an uncertainty function to express the uncertainty of the data. In implementation， the input data are also Gaussianized， and the Jensen-Shannon （JS） divergence is used to replace the Euclidean distance as the similarity matching metric in GNSOM learning， thereby obtaining the uncertainty representation. The experimental results show that GNSOM has a better training effect， and can reflect the uncertainty of the data through the covariance matrix of the neuron node. Since this Gaussization of neurons is independent of SOM itself， it can be extended to other neuron models.