Second harmonic generation (SHG) properties in two-dimensional (2D) transition-metal dichalcogenides (TMDCs) have aroused great interest. However, until now SHG for TMDC mono layer alloys is seldom investigated. Meanwhile, there is considerable controversy over the static SHG coefficients of mono layer MoS2 . The feasibility to produce terahertz (THz) radiation via SHG in pure and alloyed TMDCs has never been reported. We first calculate the SHG coefficients of mono layer MoS2 , MoSe2 , and MoS2(1-x)Se2x using the independent particle approximation plus scissors correction. We then simulate their THz absorption by applying density function perturbation theory plus the Lorentzian line and try to calculate their zero-frequency THz refractive index and birefringence. The physical property of MoS2(1-x )Se2x alloys is simulated by considering various combinations. Results indicate that mono layer MoS2, MoSe2 , and MoS2(1-x)Se2x possess large static SHG coefficients and THz birefringence and display low absorption over broadband THz frequencies. Therefore, they have applications in producing THz radiation via SHG. This study demonstrates that THz radiation can be attained in a large number of mono layers and few-layers and will extend applications of 2D materials. Moreover, it is possible to identify the magnitude of static coefficients of single-layer MoS2 by measuring THz intensities. Published by AIP Publishing.