In this paper, first-principles calculations are carried out to study the structural and electronic properties of square phase MX2 and Janus MXY (M = Mo, W; X, Y= S, Se, Te) transition metal dichalcogenide monolayers. The bandgaps of unstrained 1S-MX(2 )range from 25 to 188 meV, while the values of unstrained Janus 1S-MXY range from 30 to 165 meV. For both systems, the octagon bonds are more sensitive than the square bonds in the structure under biaxial strain. The shape of their lowest conduction band near F point is observed like a Mexican-hat and it will gradually vanish from the conduction band under increasing tensile strain. 1S-MoSe2 , 1S-MoTe2 , 1S-WS2 , 1S-WSe2 , 1S-MoSeTe, 1S-WSSe and 1S-WSeTe turn to be metallic under certain compressive strains within the range from -6% to - 3%. More importantly, Janus 1S-MXY systems intrinsically possess spin splitting due to the broken out-of-plane structural symmetry compared with 1S-MX2 . The conduction band and valence band of unstrained 1S-WSTe split about 29 meV and 31 meV, respectively. The results show that compressive strain can enhance the spin splitting and 1S-WSTe monolayer presents the largest splitting of 129 meV under - 3% compressive strain.