Network function virtualization can significantly improve the flexibility and effectiveness of network appliances via a mapping process called service function chaining. However, the failure of any single virtualized network function causes the breakdown of the entire chain, which results in resource wastage, delays, and significant data loss. Redundancy can be used to protect network appliances; however, when failures occur, it may significantly degrade network efficiency. In addition, it is difficult to efficiently map the primary and backups to optimize the management cost and service reliability without violating the capacity, delay, and reliability constraints, which is referred to as the reliability‐aware service chaining mapping problem. In this paper, a mixed integer linear programming formulation is provided to address this problem along with a novel online algorithm that adopts the joint protection redundancy model and novel backup selection scheme. The results show that the proposed algorithm can significantly improve the request acceptance ratio and reduce the consumption of physical resources compared to existing backup algorithms.