Identification of the most influential spreaders that maximize information propagation in social networks is a classic optimization problem, called the influence maximization (IM) problem. A reasonable diffusion model that can accurately simulate information propagation in social networks is the key step to efficiently solving the IM problem. Synergism of neighbor nodes plays an important role in information propagation dynamics. Some known diffusion models have considered the reinforcement mechanism in defining the activation threshold. Most of these models focus on the synergetic effects of nodes on their common neighbors, but the accumulation of synergism has been neglected in previous studies. Inspired by these facts, we first discuss the catalytic role of synergism in the spreading dynamics of social networks and then propose a novel diffusion model called the synergism-based three-step cascade model (TSSCM) based on the above analysis and the three-degree influence theory. Finally, we devise an algorithm for solving the IM problem based on the TSSCM. Experiments on five real large-scale social networks demonstrate the efficacy of our method, which achieves competitive results in terms of influence spreading compared to the four other algorithms tested.