This paper settles the nonlinear merging consensus for multi-agent systems on a directed and weighted signed network. A novel nonlinear merging control protocol is proposed to drive the states of all agents to arrive at the same state. To be consistent with the reality, the interactions among agents can be either cooperative or competitive and the information flow is considered to be directed. Particularly, the protocol can still ensure the states of all agents to reach an agreement, even though the corresponding directed network is not strongly connected. Besides, to guarantee the efficiency of multi-agent systems, the convergence rate of agents can be sped up by adjusting the parameter of the protocol. Finally, the theoretical analysis and simulation results are provided to verify the effectiveness of this protocol. The current results are instructive for us to comprehend and design an efficient consensus protocol within multi-agent systems.