In this paper, we propose a new survivable algorithm, called Enhanced Shared-Path Protection (ESPP), to tolerate multi-link failures in WDM optical networks. In ESPP, we consider the load balancing method to reduce the blocking probability for computing the primary paths, and we also use the idea of backup resources sharing to save backup resources for computing the backup paths. In order to tolerate multi-link failures, we perform the recovery escalation mechanism to establish new routes for carrying the traffic affected by the failures. Simulation results show that, compared with the conventional algorithm, ESPP has better resource utilization ratio, lower blocking probability, and higher protection ability.