This work proposes a novel variational frame- work for exemplar-based image colorization in RGB while most of existing methods use a luminance-chro- minance space. Using directly these three RGB chan- nels, our model does not need any pre or post-pro- cessing step. We design a primal-dual like algorithm that solves the proposed variational approach. The constraint when colorizing a gray-scale image is to maintain its luminance. In our RGB model this constraint is added in the variational model. Its preservation requires introducing a novel projection scheme that takes care of the hue value (H) of the HSI color-space. The behavior of our algorithm is illustrated on numerous examples, and a qualitative comparison is made with state-of-the-art methods.