Using first-principles calculations, we investigated the electronic and magnetic performance of MoTe2 monolayer doped by transition metal (TM) Ti, V, Cr, Mn, Fe, Co and Ni atoms as well as strain effects. The dopants of Ti, V, Mn, Fe, Co and Ni atoms can induce magnetic moments in MoTe2 monolayer, and the magnetic moments mainly originate from the localizing unpaired TM-3d electrons. Mn- and Fe-doped MoTe2 nanostructures show the half-metallic character with 100% spin polarization near the Fermi level. The elastic strain applied on TM-doped MoTe2 monolayer systems leads to the redistribution of the electrons in TM-3d states, which results in the magnetic state transition in doped systems. The magnetic moments of Ti-, Co- and Ni-substituted MoTe2 sheets monotonously increase with the increase in strain, while the magnetic moment of V-substituted MoTe2 sheet has an oscillatory variation with the increase in strain. The Hubbard potential U has no significant effect on our main conclusions. The research results offer an important theoretical support for further application of strain-driven spin devices on MoTe2 nanostructures.