sensitive and fast responsive X-ray detectors are crucial for safety, accuracy, and stability in medical diagnosis. To achieve high sensitivity, the thick absorption layer is used to guarantee efficient X-ray photon absorption. However, there is a significant issue that the time response of photodetectors is sacrificed for a thick absorption layer. Herein, we demonstrate the possibility to use InGaAs/InAlAs separate absorption, grading, charge, and multiplication avalanche photodiodes (SAGCM APDs) for highly sensitive X-ray detection with fast time response. Thanks to the internal multiplication, the sensitivity of the optimized device is 3.1 x 10(5) mu CGy(-1) cm(-2) under 50 keV hard X-ray radiation, which is 14000 times higher than commercial alpha-Se detectors. The 3-dB bandwidth of the APDs is 2.93 GHz, corresponding to a time response of 0.34 ns. To overcome the trade-off between sensitivity and time response, we propose a parameter named sensitivity-bandwidth product (SBP) to assess the system performance of the X-ray detector. The device exhibits a higher SBP (9.08 x 10(5) mu C middot GHz middot Gy(-1 )middot cm(-2)) than any other reported X-ray detector. Our results may provide new strategies to develop a high-performance X-ray detector in medical diagnosis.