Recently,most of works had studied the impulsive stabilization of networks with time-varying delays. But there are few results about synchronization criterion of networks with time-varying delays via adaptive-impulsive control. In this paper,by adaptive-impulsive control method,projective synchronization in the drive-response complex network of partially linear systems with time-varying coupling is investigated. An adaptive-feedback controller,updating laws and a linear impulsive controller are proposed. An adaptive-impulsive projective synchronization criterion of network with time-varying coupling is established. And the coupling configuration matrix in network is not required irreducible. Moreover,numerical simulation is used to verify the effectiveness of the scheme.