In recent years, the rapid development of the Internet has allowed people at home to access large amounts of image data stored on web servers throughout the world. Significant value can be added by estimating the illuminant at the time of acquisition, and convert to the image under a desired illuminant source. There have been studies about illuminant estimation. All of these algorithms perform illuminant estimation in an original image. This paper stands on a slight different point of view from these existing studies. The purpose of the study is to obtain an image illuminated by a desired one. In the proposed algorithm, the conversion is performed from an image whose illuminant is unknown to the image whose illuminant is the desired one. In the conversion process, the illuminant estimation is performed relative to the desired one, and the problem dimensions are reduced.The problem is formulated by an optimization problem framework of a cost function and some constraints and for the solution, a variation method is applied iterative.