The bandwidth requirement of an end-to-end request between the source and destination nodes varies dynamically with time (denoted as time-varying traffic). For serving timevarying traffic on an elastic optical network (EON), the frequency spectrum allocated for the request can be expanded or contracted to meet the bandwidth requirement. Multipath routing can reduce the blocking probability of requests for EONs, but the delay-variation between these lightpaths should be considered when establishes these lightpaths. In this paper, the Delay-Variation Constrained Spectrum Expansion and Contraction Problem (DVCSECP) for multipath routing on EONs is studied with time-varying traffic. The expansion/contraction algorithms and several path-selecting policies (PSPs) are proposed to solve this problem. Simulations show that the proposed algorithms can achieve good results.