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Color magnetic particle imaging (cMPI) is an advanced technology to distinguish different kinds of nanoparticles. This technology is realized based on the different harmonic responses and relaxation behavior of particles. However, the commonly used MPI Kaczmarz method has artifacts when it is applied to cMPI reconstruction. To address this problem, a multi-color Kaczmarz method (MKZ) is proposed for cMPI reconstruction. We introduce a new interference item to identify the artifacts caused by the interference between different particles. This method showed better performance than the Kaczmarz method in numerical experiments. It can eliminate the artifacts and efficiently improve the image quality of cMPI.