In order to characterize traps in semi-insulating 4H-SiC and HgI2 regarded as an attractive semiconductor for X-ray detectors, we apply discharge current transient spectroscopy (DCTS), which is a graphical peak analysis method based on the transient reverse current of a diode. In high-purity semi-insulating 4H-SiC whose diode may detect X-rays or γ-rays, DCTS can detect two types of trap species, and can determine those densities and emission rates. The emission rates of detected traps are close to each other, suggesting that thermally stimulated current (TSC) may not distinguish between these two types of traps. In semi-insulating HgI2, the densities and emission rates of two types of trap species are also determined by DCTS. Therefore, it is demonstrated that DCTS is a powerful method for determining the densities and emission rates of traps in semi-insulating semiconductors