With the expansion and increasing complexity of data center networks (DCNs), network fault-tolerance has become increasingly important. RRect is a server-centered DCN with a good interconnection structure. In this paper, we propose a fault-tolerant routing algorithm RRFP under a conditional fault pattern of RRect, which can find a fault-free path between any two fault-free vertices. Firstly, we study a fault pattern of RRect in the case of restricted faulty vertex sets, $\{1,2\}$-restricted connectivity. It is about $\{2,3\}$ times RRect’s traditional connectivity, indicating that $\{1,2\}$-restricted connectivity better evaluates the fault-tolerant capability. Secondly, we design an effective fault-tolerant routing algorithm RRFP under the conditional fault pattern of RRect, and RRFP can accommodate more faulty vertices. Finally, we conduct experiments on RRFP to evaluate its performance. The experimental results show that in terms of the running time, as parameters $n$ and $k$ change, RRFP outperforms Dijkstra’s algorithm by 64%–84% and Breadth-First-Search (BFS) by 56%–71%. The running time of all the three algorithms is very short as parameter $m$ changes. In terms of the constructing path length, as parameters change, RRFP outperforms BFS by 12%–19%. Moreover, the path constructed by RRFP approaches the shortest path of Dijkstra’s algorithm. Moreover, RRFP still maintains a low transmission failure rate (TFR) and high reliability even with an increase in the number of fault elements.