Ge p-i-n resonant-cavity-enhanced photodetectors (RCE-PDs) grown on silicon-on-insulator substrate are proposed and optimized at 1550 nm for high quantum efficiency and bandwidth. A vertical cavity is formed, consisting of a buried oxide as the top reflector and Si/SiO2 distributed Bragg reflector(DBR) layers as the bottom reflector, to enhance the light-matter interaction within the Ge p-i-n structure. The results demonstrate the optimized Ge RCE-PDs can achieved the quantum efficiency of 23% for the 346nm Ge thickness (34% for the 526 nm Ge thickness) and the high bandwidth of 55 GHz (47 GHz) at 1550 nm with 3 pairs Si/SiO2 DBR. These results indicate that the performance of the Ge RCE-PDs surpasses that of Ge photodetectors without RCE enhancement.