Improving universality and robustness of the control method is one of the most challenging problems in the field of complex networks (CNs) synchronization. In this paper, a special unilateral coupling finite-time synchronization (UCFTS) method for uncertain CNs is proposed for this challenging problem. Multiple influencing factors are considered, so that the proposed method can be applied to a variety of situations. First, two kinds of drive-response CNs with different sizes are introduced, each of which contains two types of nonidentical nodes and time-varying coupling delay. In addition, the node parameters and topological structure are unknown in drive network. Then, an effective UCFTS control technique is proposed to realize the synchronization of drive-response CNs and identify the unknown parameters and topological structure. Second, the UCFTS of uncertain CNs with four types of nonidentical nodes is further studied. Moreover, both the networks are of unknown parameters, time-varying coupling delay and uncertain topological structure. Through designing corresponding adaptive updating laws, the unknown parameters are estimated successfully and the weight of uncertain topology can be automatically adapted to the appropriate value with the proposed UCFTS. Finally, two experimental examples show the correctness of the proposed scheme. Furthermore, the method is compared with the other three synchronization methods, which shows that our method has a better control performance.