The k-ary n-cube Qkn （n ≥2 and k ≥3） is one of the most popular interconnection networks. In this paper, we consider the problem of a fault- free Hamiltonian cycle passing through a prescribed linear forest （i.e., pairwise vertex-disjoint paths） in the 3-ary n-cube Qn^3 with faulty edges. The following result is obtained. Let E0 （≠θ） be a linear forest and F （≠θ） be a set of faulty edges in Q3 such that E0∩ F = 0 and ｜E0｜ ＋｜F｜ ≤ 2n - 2. Then all edges of E0 lie on a Hamiltonian cycle in Qn^3- F, and the upper bound 2n - 2 is sharp.
