This paper is concerned with the winner-take-all (WTA) problem on networks. We propose the first distributed protocol to address this problem dynamically. This protocol features strong nonlinearity. Theoretical analysis reveals that it contains invariant quantities, symmetric solutions, and multiple equilibrium points. By leveraging these properties, this work proves the instability of its non-WTA solutions, and global convergence to the WTA solution via Lyapunov theory. Two simulations over networks with 10 and 200 nodes, respectively, are conducted. Simulation results have well verified the theoretical conclusions drawn in this paper.