In this paper, we aim to study Kronecker canonical form theory for T-type digraphs, which can be used to construct trees by tensor product with some directed paths. Firstly, we show that some bicyclic digraphs and multicyclic digraphs are T-type digraphs. Secondly, we provide a characterization for T-type digraphs by their Kronecker canonical form. Moreover, we present an algorithm for computing the Kronecker canonical form, which can be used to determine whether or not a digraph is a T-type digraph. Lastly, for a class of T-type digraphs, we show that their incidence matrix pair can be transformed into Kronecker canonical form using unimodular matrices. We also present an algorithm related to finding such unimodular matrices.