A three-valued function f defined on the vertices of a digraph D = (V, A), $f:V{ ightarrow}{-1,0,+1}$ is a minus total dominating function(MTDF) if $f(N^-(v)){geq}1$ for each vertex $v{in}V$. The minus total domination number of a digraph D equals the minimum weight of an MTDF of D. In this paper, we discuss some properties of the minus total domination number and obtain a few lower bounds of the minus total domination number on a digraph D.