The paper describes a nonlinear approach for constructing color conversions based on radial basis functions (RBFs). The RBF is embedded in a two-layer structure that uses a linear transfer function for the output units and a nonlinear transfer function for the hidden units. RBFs are popular for interpolating scattered data as the associated system of linear equations is guaranteed to be invertible under very mild conditions on the locations of the data points. In particular, RBFs do not require that the data lie on any sort of regular grid. The purpose of using RBFs in color conversion is to improve the accuracy, efficiency, and performance of optimization and interpolation for high-dimensional non-linear scattering data. This approach is practical with color conversions for color devices, which have nonlinear behavior, for example, color printers. Preliminary results have shown that the RBF color mapping technique can be very effective in reducing the maximum errors of color conversions. In one experiment we observed that the maximum error was reduced by half.