A method is proposed for solving the mapping problem from the three-dimensional color space to the four-dimensional CMYK space of printer ink signals by means of a neural network. The CIE-L*a*b* color system is used as the device-independent color space. The color reproduction problem is considered as the problem of controlling an unknown static system with four inputs and three outputs. A controller determines the CMYK signals necessary to produce the desired L*a*b* values with a given printer. Our solution method for this control problem is based on a two-phase procedure which eliminates the need for UCR and GCR. The first phase determines a neural network as a model of the given printer, and the second phase determines the combined neural network system by combining the printer model and the controller in such a way that it represents an identity mapping in the L*a*b* color space. Then the network of the controller part realizes the mapping from the L*a*b* space to the CMYK space. Practical algorithms are presented in the form of multilayer feedforward networks. The feasibility of the proposed method is shown in experiments using a dye sublimation printer and an ink jet printer.