Given a directed graph $G$ with non negative cost on the arcs, a directed
tree cover of $G$ is a directed tree such that either head or tail (or both of
them) of every arc in $G$ is touched by $T$. The minimum directed tree cover
problem (DTCP) is to find a directed tree cover of minimum cost. The problem is
known to be $NP$-hard. In this paper, we show that the weighted Set Cover
Problem (SCP) is a special case of DTCP. Hence, one can expect at best to
approximate DTCP with the same factor as for SCP. We show that this expectation
can be satisfied in some way by designing a purely combinatorial approximation
algorithm for the DTCP and proving that the approximation factor of the
algorithm is $\max(2, \ln(D^+))$ with $D^+$ is the maximum outgoing degree of
the nodes in $G$.