Given a directed graph
with non-negative cost on the arcs, a directed tour cover
is a cycle (not necessary simple) in
such that either head or tail (or both of them) of every arc in
is touched by
. The minimum directed tour cover problem (DToCP) which is to find a directed tour cover of minimum cost, is
-hard. It is thus interesting to design approximation algorithms with performance guarantee to solve this problem. Although its undirected counterpart (ToCP) has been studied in recent years [1,6], in our knowledge, the DTCP remains widely open. In this paper, we give a 2log
)-approximation algorithm for the DTCP.