Distilling quantum coherence is important for optimizing the performance of quantum technologies, however, it cannot always be accomplished with certainty. Then, the probabilistic distillation of quantum coherence has been developed and successfully implemented in experiments. We introduce a proposal to realize the one-shot coherence distillation in the superconducting circuit system. The target maximally coherent state can be extracted from a single copy of the prepared state by using appropriate incoherent operations and a finite error tolerance is allowed. It is easy to implement our scheme in the experiment that only a superconducting qubit is required to be the auxiliary system. To demonstrate the feasibility of our scheme, we numerically simulate the distillation process under the influence of dephasing (according to the typical experimental parameters). We find that the distillation rate of the coherence resource can be well achieved with the current experimental technique.