  Suzuki (2004) [7] classified thin weakly distance-regular digraphs and pro-
posed the project to classify weakly distance-regular digraphs of valency 3.
The case of girth 2 was classified by the third author (2004) [9] under the
assumption of the commutativity. In this paper, we continue this project and
classify these digraphs with girth more than 2 and two types of arcs.
