The color transfer problem aims at generating an image by changing the colors of a target image with new colors of a given reference image. In this manuscript, we introduce a novel fractional-order total variation-based model for the color transfer problem. The proposed model extends the total generalized variation-based model, by adding a new data fidelity term and changing the regularization term. These terms enable the reduction of color artifacts and keep the structures of a target image well. To solve our model, we adopt the forward--backward splitting algorithm, and the alternating direction method of multipliers is used for solving subproblems. Numerical experiments validate the effectiveness of the proposed model compared to the existing methods.