The folded hypercube is a well-known variation of hypercube structure and can be constructed from a hypercube by adding a link to every pair of vertices with complementary addresses. An n-dimensional folded hypercube (FQn for short) for any odd n is known to be bipartite. In this paper, let f be a faulty vertex in FQn. It has been shown that (1) Every edge of FQn−{f} lies on a fault-free cycle of every even length l with 4≤l≤2n−2 where n≥3; (2) Every edge of FQn−{f} lies on a fault-free cycle of every odd length l with n+1≤l≤2n−1, where n≥2 is even. In terms of every edge lies on a fault-free cycle of every odd length in FQn−{f}, our result improves the result of Cheng et al. (2013) where odd cycle length up to 2n−3.