The $h$-restricted edge connectivity is an important parameter in measuring the reliability and fault tolerance of large interconnection networks. Let $G$ be a connected graph and $h$ be a non-negative integer. The $h$-restricted edge connectivity of $G$ is the minimum cardinality of a set of edges, if it exists, whose deletion disconnects $G$ and the degree of each vertex in every remaining component is at least $h$. The $n$-dimensional folded crossed cube is obtained from the $n$-dimensional crossed cube by adding extra edges. The $h$-restricted edge connectivity, which is an important measure in evaluating the reliability, is utilized to analyze the reliability of folded crossed cube. Then the $h$-restricted edge connectivity of folded crossed cubes is obtained. Finally, it is proved that the $2$-restricted edge connectivity of a folded crossed cube is equal to $4n-4 (n\geq 4)$. It means that at least $4n-4$ edges must be removed to disconnect a $n$-dimensional folded crossed cube, provided that the removal of these vertices does not leave a vertex that has degree less than two.