Accurate estimation of the merger timescale of galaxy clusters is important to understand the cluster merger process and further the formation and evolution of the large-scale structure of the universe. In this paper, we explore a baryonic effect on the merger timescale of galaxy clusters by using hydrodynamical simulations. We find that the baryons play an important role in accelerating the merger process. The merger timescale decreases with increasing the gas fraction of galaxy clusters. For example, the merger timescale is shortened by a factor of up to 3 for merging clusters with gas fractions 0.15, compared with the timescale obtained with zero gas fractions. The baryonic effect is significant for a wide range of merger parameters and especially more significant for nearly head-on mergers and high merging velocities. The baryonic effect on the merger timescale of galaxy clusters is expected to have impacts on the structure formation in the universe, such as the cluster mass function and massive substructures in galaxy clusters, and a bias of no-gas may exist in the results obtained from the dark matter-only cosmological simulations.