There are very complicated nonlinear relations between input value and presentation color of digital prepress devices, as well as in the gamut mapping among different devices. Not all the relations can be described by linear model properly. In recent years, neural network and black box theory are introduced to describe the relations. In this research, the printer gamut is divided into micro space sections, a relative colorimetric rending mapping method is proposed based on BP neural network theory to complete the gamut mapping from monitor gamut to color printer. Experimental results show that the model reduces the color error of color blocks between the two devices, and the color rendering method can be used for gamut mapping of image with less continuous tone.