Low energy X-ray telescope, working over 0.7-15 keV energy band, is one of the main payloads in the hard X-ray modulation telescope satellite. The primary scientific objectives are to survey large sky area to investigate galactic X-ray transient sources as well as the cosmic X-ray background, and to observe X-ray binaries or black holes for studying the dynamics and emission mechanism in strong gravitational or magnetic field. The detector of low energy X-ray telescope is CCD236, a new generation of swept charge device, which has good time and energy resolution. Quantum efficiency (QE) of the detector has a crucial influence on X-ray spectrum fitting and absolute luminosity calculation. To provide valuable scientific data, QE should be calibrated in detail. In this paper, QE calibration is accomplished with respect to a silicon drift detector (SDD), using an Fe-55 radioactive source, at energy points Mn-Kα (5.899 keV) and Mn-Kβ (6.497 keV). The energies of Mn-Kα and Mn-Kβ are near that of iron-K, which is an important line in X-ray observation. Additionally, Mn-Kα and Mn-Kβ X-ray will partially pass through the depletion region of CCD236, and these energy points can be used to measure the depletion thickness. This experiment is set up in a vacuum cooling chamber. The X-ray source perpendicularly illuminates SDD and CCD236 through a small hole, whose area is far less than those of two detectors; therefore, QE measurements are irrelevant to neither the distance nor the azimuth angle between the X-ray source and the detector. For CCD236, split events should be corrected. Energy spectra of SDD and CCD236 are fitted with two Gaussian distributions, respectively, to obtain peak positions and standard variations of Mn-Kα and Mn-Kβ. With known structure of SDD, the QE of CCD236 can be calculated. QE values at Mn-Kα and Mn-Kβ are 71% and 62%, respectively. QE and temperature are uncorrelated with each other in a temperature range from -95 ℃ to -30 ℃. According to the specific structure of CCD236 and the measured QE, without considering the effect of channel stop, the best-fit thickness of depletion region is obtained to be 38 μm. When CCD236 is applied with different driving or substrate voltages, no obvious variation of QE is observed. It indicates that the thickness values of depletion region with high and low level voltages are equal. Furthermore, it shows that working CCD236 is deep depleted, and the thickness of depletion region will not change because it reaches its maximum, the edge of epitaxial layer and substrate layer.