X-ray diagnosis is a crucial aspect of nuclear experiments, as many fields in physical research require X-ray analysis. The X-ray diode (XRD) detector is commonly used in X-ray detection due to its short response time, necessitating a high-speed readout circuit. In this paper, we present the design of an X-ray diagnosis system with readout electronics utilizing time-interleaved analog-to-digital converters (TIADC). One of the challenging problems in TIADC is the mismatch problem between channels, which severely reduces the system's performance. We propose a fast calibration method for adjusting the mismatch, significantly improving the acquisition system's performance. We have implemented an adapted module to perform the calibration in real-time. In performance tests, the proposed method is shown to be as effective as other methods, and the electronic performance of the system meets the diagnosis requirements. The X-ray signals acquired by this system exhibit high quality in the inertial confinement fusion (ICF) of the SG-III laser facility.