In this paper, the adaptive synchronisation of time-varying perturbed complex networks with non-dissipatively coupled and uncertain inner coupling matrix is studied. In order to describe the actual network better, the out-coupling configuration matrix is not limited by the dissipatively coupled conditions. It is also worth pointing out that the drive system and the response system described in this paper are uncertain, and uncertainty arises in linear inner coupling matrix and unavoidable uncertain external disturbances, which is different from the past. On the basis of Lyapunov stability theory, adaptive law can be obtained and at the same time unknown bounded disturbances can be overcome.