In radar, communication and other engineering applications, fast synchronization is needed because of the limited time of transmitting signal. However, the convergence rate of conventional synchronization is slow. To resolve the problem, a fast synchronization algorithm is proposed. According to Taylor expansion, nonlinear controller is designed to make the control matrix of error equation satisfy critical conditions for synchronization and further to optimize the control matrix, so fast synchronization can be achieved with only one step operation. In addition, given the practical engineering launches only one state variable, in this paper are take the typical continuous Duffing system and discrete Logistic system as examples and design the fast synchronization driven by only one variable. Finally, simulation results show that compared with common single coupling and OPCL synchronization, the proposed algorithm has fast convergence rate, strong anti-noise cap ability, and strong engineering practice significance.