The cross coupling of the C-OMe bond adjacent to a nitrogen atom in dialkoxy-N,N-dialkylmethanamines with terminal alkynes was efficiently approached in the presence of copper catalyst under mild conditions to give 3-amino-1,4-diynes in good yields. The reaction is promoted by phosphine ligands and the chemistry provides a simple and efficient route to 3-amino-1,4-diynes. Importantly, the Michael addition occurred with as-prepared 3-amino-1,4-diynes to give the useful Michael-adducts containing tert-alkylamines in a very convenient way. Further studies revealed that (E)-1,5-diarylpent-1-en-4-yn-3-one was formed through the rearrangement by using the neutral alumina column, and the corresponding imine 2-(1,5-diphenylpent-2-en-4-ynylideneamino)ethanol was obtained in the presence of AgOTf.