This paper investigates the cluster synchronisation problem for multi-agent non-zero sum differential game with partially unknown dynamics. The objective is to design a controller to achieve the cluster synchronisation and to ensure local optimality of the performance index. With the definition of cluster tracking error and the concept of Nash equilibrium in the multi-agent system (MAS), the previous problem can be transformed into the problem of solving the coupled Hamilton-Jacobi-Bellman (HJB) equations. To solve these HJB equations, a data-based policy iteration algorithm is proposed with an actor-critic neural network (NN) structure in the case of the MAS with partially unknown dynamics; the weights of NNs are updated with the system data rather than the complete knowledge of system dynamics and the residual errors are minimised using the least-square approach. A simulation example is provided to verify the effectiveness of the proposed approach.