Abstract: A design scheme of a distributed radial basis for neural network （RBFNN）adaptive controller with similar parameters is proposed for a class of consitency problem of nonlinear multi-agent system with heterogeneity in different dimensions. The definition of nonlinear multi-agent system with heterogeneity in different dimensions is addressed, on this basis, the similar properties and the similar parameters existing in each agent are presented, the universal approximation properties of RBFNN is combined, a scheme of a novel distributed feedback adaptive neural network controller is devised based on the design of some adaptive laws of coupling weights among each agent. The design method can guaranteem all the states of nonlinear multi-agent system with heterogeneity in different dimensions are consistent, and make all signals in the closed-loop systems to be meet with the conditions of uniformly ultimately bounded（UUB） . The design of the control approach can breaks the limition of the same dimension of each subsystem in the traditionally heterogeneous multi-agent, the design method of controller is not only suitable for to a kind of heterogeneous multi-agent systems with same dimension, but also be applicable in heterogeneous multi-agent with different dimensions. Finally, two simulation examples are utilized to verify the effectiveness of the proposed design method of the controller.