The Bayes Principal components Backpropagation Network (BPBN) is proposed to retrieve total precipitable water (TPW) from the AMSR2 instrument on-board recently launched GCOM-W1 satellite. The proposed algorithm is a physical inversion method, developed using a radiative transfer model to assure that the geophysical retrieval of the TPW is consistent with the radiative transfer theory. The algorithm is comprised of- a Bayes variational algorithm for bias correction, the principal components transformation of the bias-corrected radiometric brightness temperature, and finally, a Bayesian regulation backpropagation network to translate the principal components to TPW estimate in the geophysical space. The algorithm is applicable over ocean, and in clear and cloudy scenes. However, the rainy and sea ice scenes are excluded in the retrieval. A random forest classifier and NASA sea ice temperature retrieval algorithm are used to detect and suppress the rainy and sea ice scenes, respectively. On the whole, the BPBN is a “comprehensive” algorithm, from discarding the redundant scenes to transforming the radiometric information to TPW estimate, and doesn’t use any auxiliary data. This will make it very useful for assimilating into the numerical weather prediction models. The retrieval accuracy of the BPBN algorithm is around 2 $\hbox{kg/m}^2$ .