Remote sensing of global ocean color is a valuable tool for understanding the ecology and biogeochemistry of the worlds oceans, and provides critical input to our knowledge of the global carbon cycle and the impacts of climate change. Ocean polarized reflectance contains information about the constituents of the upper ocean euphotic zone, such as colored dissolved organic matter (CDOM), sediments, phytoplankton, and pollutants. In order to retrieve the information on these constituents, remote sensing algorithms typically rely on radiative transfer models to interpret water color or remote-sensing reflectance; however, this can be resource-prohibitive for operational use due to the extensive CPU time involved in radiative transfer solutions. In this work, we report a fast model based on machine learning techniques, called Neural Network Reflectance Prediction Model (NNRPM), which can be used to predict ocean bidirectional polarized reflectance given inherent optical properties of ocean waters. This supervised model is trained using a large volume of data derived from radiative transfer simulations for coupled atmosphere and ocean systems using the successive order of scattering technique (SOS-CAOS). The performance of the model is validated against another large independent test dataset generated from SOS-CAOS. The model is able to predict both polarized and unpolarized reflectances with an absolute error (AE) less than 0.004 for 99% of test cases. We have also shown that the degree of linear polarization (DoLP) for unpolarized incident light can be predicted with an AE less than 0.002 for 99% of test cases. In general, the simulation time of SOS-CAOS depends on optical depth, and required accuracy. When comparing the average speeds of the NNRPM against the SOS-CAOS model for the same parameters, we see that the NNRPM is able to predict the Ocean BRDF 6000 times faster than SOS-CAOS. Both ultraviolet and visible wavelengths are included in the model to help differentiate between dissolved organic material and chlorophyll in the study of the open ocean and the coastal zone. The incorporation of this model into the retrieval algorithm will make the retrieval process more efficient, and thus applicable for operational use with global satellite observations.