  We propose a new multi-component two-dimensional Toda lattice hierarchy
(mc2dTLH) which includes two-dimensional Toda lattice equation with
self-consistent sources (2dTLSCS) as the first non-trivial equation. The Lax
representations for this mc2dTLH are presented. We construct a
non-auto-B\"acklund Darboux transformation (DT) for 2dTLSCS by applying the
method of variation of constant (MVC) to ordinary DT of 2dTLSCS. This
non-auto-B\"acklund DT enables us to obtain various solutions such as solitons,
rational solutions etc., to 2dTLSCS.
