Recovery from a link or node failure in the internet is often subjected to seconds or minutes of routing convergence, during which certain end-to-end connections may experience seconds or minutes of outage. According to this problem, existing approaches reroute the data traffic to a pre-defined backup path to detour the failed components. However, the maintenance of backup path increases the significant bandwidth expenditure. On the other hand, the diverted traffic may cause congestion on the backup path if it is not carefully split over multiple paths according to their available capacity. In this paper, we propose an efficient recovery scheme by using one-hop overlay multipath source routing, which is a post-failure recovery method. Once a failure happens, multiple one-hop overlay paths are constructed by selecting strategically multiple relay nodes, and the affected traffic is diverted to these paths in a well-balanced manner. We formulate the traffic allocation problem as a tractable linear programming (LP) optimisation problem, whose goal is to minimise the worse-case network congestion ratio. Simulations based on a real ISP network and a synthetic internet topology show that our scheme can effectively balance link utilisation dramatically and improve the reliability of network.