We report a theoretical study of a broadband Si/graded-SiGe/Ge/Ge0.9Sn0.1 p-i-n photodetector with a flat response based on modulating thickness of the layers in the active region.The responsivity of the photodetector is about 0.57 A/W in the range of 700 to 1800 nm.This structure is suitable for silicon-based epitaxial growth.Annealing is technically applied to form the graded-SiGe.The photodetector reaches a cut-off wavelength at ～2300 nm and a low dark-current density under 3 V reverse bias about 0.17 mA/cm2 is achieved theoretical at room temperature.This work is of great significance for silicon-based detection and communication,from visible to infrared.