Group-IV GeSn material systems have recently considered as a new material for sensitive photodetection in the short-wave infrared (SWIR) region. The introduction of Sn into Ge can effectively narrow the bandgap energies, thereby extending the absorption edges toward the longer wavelengths and enabling effective photodetection in SWIR region. Here we present an experimental and modeling study of GeSn/Ge quantum well (QW) photodetectors on silicon substrates for effective SRIW photodetection. Epitaxial growth of pseudomorphic GeSn/Ge QW structures was realized on Ge-buffered silicon substrates using low-temperature molecular beam epitaxy. Normal incident GeSn/Ge QW photodetectors were then fabricated and characterized. The optical responsivity experiments demonstrate that the photodetection cutoff wavelengths is extended to beyond 1800 nm, enabling effective photodetection in SWIR spectral region. We then develop theoretical models to calculate the composition-dependent strained electron band structures, oscillation strengths, and optical absorption spectra for the pseudomorphic GeSn/Ge QW structures. The results show that Ge1-xSnx well sandwiched by Ge barriers can achieve a critical type-I alignment at Γ point to provide necessary quantum confinement of carriers. With an increase in the Sn content, the band offsets between the GeSn well and Ge barreirs increases, thus enhancing the oscillation strengths of direct interband transitions. In addition, despite stronger quantum confinement with increasing Sn content, the absorption edge can be effectively shifted to longer wavelengths due to the direct bandgap reduction caused by Sn-alloying. These results suggest that GeSn/Ge QW photodetectors are promising for low-cost, high-performance SWIR photodetection applications.