Consensus problem for multi-agent systems has become a hot topic in the control community, and many research achievements have been reported. Most of the literatures mainly consider the case of linear algorithms and measurable agent states, but it is difficult to measure states of the agents directly in some real applications. Consensus problem for second-order, multi-agent systems with nonlinear output network is studied in the paper. To the multi-agent system difficult to measure directly, a consensus protocol design method is proposed respectively for second-order, multi-agent systems with a leader and without a leader. Consensus convergence is proved by using invariant set theorem, and the decision value is derived for the case of multi-agent system without a leader. Finally, the numerical simulations and analysis on different conditions are given to verify the effectiveness of theoretical results.