The bandwidth required of time-varying traffic changes with time. How to allocate bandwidth and choose survivable transmission lightpath for time-varying traffic poses a great challenge to the performance of elastic optical networks. In this paper, a survivable time-varying traffic spectrum allocation based on center fit spectrum allocation with quasi-center spectrum expansion/contraction (STTSA-CFSA-QCSEC) algorithm is proposed for time-varying traffic in survivable elastic optical networks. Specifically, we focus on how to allocate varying bandwidth for time varying traffic in a survivable elastic optical network. Considering the characteristics of time-varying traffic and the direction of bandwidth variation for time-varying traffic, we propose a spectrum allocation policy different from that of traditional fixed-bandwidth requests. At the same time, for reducing the overhead of protecting bandwidth, a survivable single/dual lightpath hybrid policy is designed. Simulation results show that the proposed algorithm can effectively reduce the bandwidth blocking probability and improve spectrum utilization of elastic optical networks.