In this paper, we proposed a fast recovery strategy for a dual link failure (DLF) in elastic optical network (EON). The EON is a promising solution to meet the next generation higher bandwidth demand. The survivability of high speed network is very crucial. As the network size increases the probability of the DLF and node failure also increases. Here, we proposed a parallel cross connection backup recovery strategy for DLF in the network. The average bandwidth blocking probability (BBP), bandwidth provisioning ratio (BPR), and recovery time (RT) for our proposed Intermediate node cross-connect backup for shared path protection (INCB-SPP) for ARPANET are 0.38, 2.71, 4.68 ms, and for DPP 0.70, 6.02, 8.71 ms and for SPP 0.40, 2.87, and 16.33 ms respectively. The average BBP, BPR, and RT of INCB-SPP for COST239 are 0.01, 1.71, 3.79 ms and for DPP are 0.39, 3.50, 8.20 ms and SPP are 0.04, 1.75, and 12.47 ms respectively. Hence, the proposed strategy shows lower BBP, fast connection recovery, and BPR when compared with the existing shared path protection (SPP) and dedicated path protection (DPP) approaches. Simulation is performed on ARPANET and COST239 topology networks.