The volumetric display technology is one of the important science frontiers of modem society. Multi-photon up-conversion volumetric 3-D display, attractive especially in its self-spatial vision, has the advantages of total-solidification, high reliability and speedy operation so that it has a broad range of applications. The up-conversion luminescence of oxyfluoride glass material Er(0,5): FOG, when excited by 1 520 nm semiconductor laser, was studied. The common-fluorescence spectra were measured also, in order to know up-conversion sufficiently. It was found that there are several up-conversion luminescence lines (407.43, 411.20 nm), (522.51(m), 528.57 nm), (540.53(m), 543.70, 549.00 nm), (654.75(m), 665.50 nm) and 802.10(m) nm, which can be recognized as the fluorescence-transitions of ((2)G(4) F-2 H)(9/2) --> I-4(15/2), H-4(11/2) --> I-4(15/2), S-4(3/2) --> I-4(15/2), F-4(9/2) --> I-4(15/2) and I-4(9/2) --> I-4(15/2) respectively. It is interesting that the slopes of log F-log P curves, the double logarithmic variation of up-conversion luminescence intensity F with the laser power P, are various for these observed up-conversion luminescences, which are valuable for volumetric display. The comprehensive analysis found that the ((2)G(4) F-2 H)(9/2) --> I-4(15/2) up-conversion luminescence is a four photon up-conversion luminescence, while {H-2(11/2) --> I-4(15/2), S-4(3/2) --> I-4(15/2) and F-4(9/2) I-4(15/2)} up-conversion luminescence is three-photon up-conversion luminescences, and I-4(9/2) --> I-4(15/2) up-conversion luminescence is a two-photon up-conversion luminescence. It was found also that the absorption from the groundstate I-4(15/2) level to first excited level is very large, resulting in the fact that the sequential energy transfer and step-by-step absorption up-conversion are readily to happen.