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The coherence transformation and distillation for a class of special mixed coherent states of rank-2 under incoherent operations (IO) is discussed. Similar to the entanglement transformation for mixed entangled states, the catalytic coherence transformation for this class of special mixed coherent states is analyzed. On the one hand, it is found that some of the mixed coherent states can be converted into other mixed coherent states under IO. But for those mixed coherent states which fail in the coherence conversion under IO, the catalytic coherence manipulation can solve this problem. In this case, a mixed coherent state cannot be converted into another under IO, while the coherence transformation can be realized with the help of coherence-assisted incoherent operations, that is, catalytic coherence transformation. On the other hand, these special mixed coherent states can be distilled into the maximally pure coherent states or mixed states of arbitrary dimensions by strictly incoherent operations with certain probabilities. Finally, the coherence transformation of this type of mixed states can be generalized to the case of higher rank in a similar way, which is discussed at the end of this paper.