GeSn is an attractive semiconductor material for Si-based photonics. However, large lattice mismatch between GeSn and Si and the low solubility of Sn in Ge limit its development. In order to obtain high Sn-content GeSn on Si, it is normally grown at low temperature, which would lead to inevitable dislocations. Here, we reported a single-crystal defect-free graded GeSn on insulator (GSOI) stripes laterally grown by rapid melting growth (RMG). The Sn-content reaches to 14.2% at the end of the GSOI stripe. Transmission electron microscopy observation shows the GSOI stripe without stacking fault and dislocations. P-channel pseudo metal-oxide-semiconductor field effect transistors (MOSFETs) and metal-semiconductor-metal (MSM) Schottky junction photodetectors were fabricated on these GSOIs. Good transistor performance with a low field peak hole mobility of 402 cm2/Vs is obtained, which indicates a high-quality of this GSOI structure. Strong near-infrared and short-wave infrared optical absorption of the MSM photodetectors at 1550 nm and 2000 nm were observed. Owing to high Sn-content and defect-free, responsivity of 236 mA/W@-1.5 V is achieved at 1550 nm wavelength. In addition, responsivity reaches 154 mA/W@-1.5 V at 2000 nm with the optical absorption layer only 200 nm-thick, which is the highest value reported for GeSn junction photodetectors until now.