In the process of social opinion evolution, the delay in information transmission and the asynchrony of individual updates can lead to lag errors, which affect the accuracy of opinion evolution analysis. To address this issue, this paper proposes a new competitive model based on k-winners-takes-all (k-WTA) network, which is used to describe and analyze the dynamic evolution of opinions in social networks. This model not only effectively eliminates lag errors but also takes into account the potential weight-unbalanced communication topology within real-world social networks. Furthermore, it supports distributed opinion exchange and evolution, enhancing the model’s applicability in real-world scenarios. Finally, simulations further validate the effectiveness and feasibility of this model.