Transient voltage instability is one of the important factors that threaten the stability of power system. The dynamic reactive power reserve and supporting capacity of the power grid with a high proportion of renewables decrease sharply, and the control models and operation characteristics of grid-connected renewables are diverse. Thus, the reactive power voltage of the system often fluctuates rapidly after a fault occurs, which leads to a more prominent voltage stability problem. In response, a transient voltage instability identification method based on the Koopman operator is proposed in this paper to avoid power system outage accidents caused by voltage instability in time. Firstly, the Koopman operator extraction method of Hankel matrix enhanced dynamic mode decomposition (HeDMD) is proposed with short-time wide-area measurement data after fault. Secondly, the amplitude of the Koopman operator is defined, and the dominant Koopman mode is obtained in descending order. Then, based on the time domain prediction signal of the dominant Koopman mode, the maximum Lyapunov exponent (MLE) is calculated to identify transient voltage instability. Finally, the effectiveness of the proposed method is verified using the Nordic32 test system and the standard system of China Electric Power Research Institute. Compared with the traditional method, the proposed method has more advantages in accuracy and rapidity of transient voltage instability identification. The simulation experiments prove its applicability in power grid with a high proportion of renewables.