To pursue the advanced properties of 2D materials, we explore the single-layer WSe2, one of the most studied transitional metal chalcogenide-based magnetic structures. Based on the first-principle calculations, we predict the excellent ferromagnetic coupling between the doped Cu and its nearby Se and W atoms in the single-layer WSe2 (SL-WSe2). Our calculations point out that the Cu-d electrons and the interactions between the dopant and the nearby atoms are the major cause for the induced magnetism. The emerging electronic states around the Fermi level, arising from the doped Cu and its nearby W and Se atoms, not only introduce magnetism into SL-WSe2, but also low its energy gap largely. We also demonstrate a semiconducting-metallic transition in the Cu-doped SL-WSe2 caused by the applied compressive strain and a semiconducting-half metal transition under the applied tensile strain. Moreover, we show the feasibility of doping concentrations and external strain on manipulating the conductivity and magnetism of the Cu-doped SL-WSe2.