Considering the time-varying general singular system, by using the analysis method of singular Lyapunovinequality and restrained equal transformation，the concept of admissibility and quadratic admissibility for the time-varying general singular system is proposed, a Lyapunov inequality for time-varying general singular system is established, the problem of admissibility for time-varying general singular system is transformed into solving the Lyapunov inequality problem. The necessary and sufficient conditions of admissibility and quadratic admissibility are obtained for the system. The conclusions of admissibility research achievements are natural extend from singular system to the time-varying general singular system. Finally, a numerical example is provided to demonstrate the effectiveness of the obtained conclusions.