Band gap engineering of atomically thin two-dimensional layered materials is critical for their applications in nanoelectronics, optoelectronics, and photonics. Here we report, for the first time, a simple one-step chemical vapor deposition approach for the simultaneous growth of alloy MoS2xSe2(1-x) triangular nanosheets with complete composition tunability. Both the Raman and the photoluminescence studies show tunable optical properties consistent with composition of the alloy nanosheets. Importantly, all samples show a single bandedge emission peak, with the spectral peak position shifting from 668 nm (for pure MoS2) to 795 nm (for pure MoSe2), indicating the high quality for these complete composition alloy nanosheets. These band gap engineered 2D structures could open up an exciting opportunity for probing their fundamental physical properties in 2D and may find diverse applications in functional electronic/optoelectronic devices.