Despite the importance of single-crystal elastic constants of β-phase titanium alloys in understanding their low Young's modulus—a property crucial for many applications, such data are often difficult to obtain when the alloy composition is close to the instability limit of the β phase, where the presence of α" martensite precludes the fabrication of β-phase single crystal. In the present study, we extracted the single-crystal elastic constants of such a β-phase titanium alloy with low Young's modulus, Ti-36Nb-5Zr (wt. %), from polycrystalline specimens by using an in-situ synchrotron X-ray diffraction technique. It is indicated that the low Young's modulus of the alloy originates from the anomalously low shear modulus C44 as well as the low shear modulus C', which is different from a common viewpoint that the Young's modulus of β-phase titanium alloys is dominantly controlled by the C'. This suggests that low C44 is an important contributor to low Young's modulus for instable β-phase titanium alloys.