In this work, GeSn lateral p-i-n photodetectors (PDs) on insulator were fabricated with an active GeSn layer grown by the rapid melting growth (RMG) method. Taking advantages of the defect-free GeSn strips, GeSn PDs with 5.3% Sn content have low dark current and high responsivities, which are about 0.48, 0.47, and 0.24 A/W for wavelengths of 1550, 1630, and 2000 nm, respectively. The radio frequency of the lateral GeSn PDs was also studied and a 3 dB bandwidth of about 3.8 GHz was achieved. These results indicate that the GeSn grown by the rapid melting growth method is capable of fabricating high-performance Si-based optoelectronic devices.