This paper investigates the bipartite quasi-consensus for a class of second-order heterogeneous nonlinear multi-agent systems with unknown dynamics. Based on the neural network approximation theory, a new neuro-adaptive controller is designed to ensure all agents can eventually converge to a bounded region of the leader. Several sufficient conditions of quasi-consensus and the upper bounds of error for the multi-agent systems are obtained with the help of the Lyapunov stability theorem and inequality technique. Finally, some numerical simulations are provided to illustrate the feasibility and practicality of the theoretical results.