In social systems, agents often have different ability to persuade neighbors to adopt their opinions. In this paper, we aim to investigate how the location and heterogeneity of influencers in social networks can improve convergence. We propose a voter model with dynamic self-conviction and heterogeneous individual influence which is related to the underlying network topology. An agent may keep its current opinion according to personal conviction, or otherwise, it may preferentially choose the opinion of the neighbor that has a great influence. Individual conviction evolves during the dynamic process, and can be strengthened by social recognition. Simulations indicate our model has three nontrivial results. First, the conservation of average magnetization in the voter model is broken under the effect of individual conviction and influence, and the system evolves to an ordered state in which one opinion is dominant, but total consensus is prevented by extremists. Furthermore, individual influence has a subtle action on opinion evolution. The heterogeneity of individual influence accelerates the relaxation process, but, with the action of dynamic conviction, more heterogeneous influence does not mean the average magnetization will be more ordered. In addition, when competing with agents’ conviction, more heterogeneous individual influence plays a more significant role in agents’ decisions. These results are helpful for understanding some aspects of collective phenomena that occur on online social media.