The model R5912-20MOD photomultiplier tube(PMT) is made for cryogenic application by Hamamatsu. In this paper, we report on the measurement of relative quantum efficiency (QE) of this model PMT at liquid argon(LAr) temperature. Furthermore, a specially designed setup and relevant test method are introduced. The relative QE is measured in visible wavelengths with the PMT emerged in high purity nitrogen atmosphere. The results show that the change of QE at LAr temperature is within about 5% compared with room temperature around 420 nm. However, the QE increases about 10% in the shorter wavelength range and decreases significantly after 550 nm.