In this study, by a conventional melt quenching method, we synthesized novel up-conversion phosphors of 60TeO2–30TlO0.5–(9−x)ZnO–xTm2O3–1Yb2O3 (x = 0.1–0.5) glasses, whose system was recently developed in our collaborative group, and their blue up-conversion photoluminescence (UCPL) of Tm3+ ions via three-step energy transfer from near-infrared (NIR) sensitizer of Yb3+ ions was observed. In particular, the substantial rate of the energy transfer <γd5> in the third step from Yb3+ to Tm3+ under excitation at 975 nm, which determined the final blue UCPL intensity, was estimated as a function of the rare-earth concentration. With an aid of analytical methods of PL lifetime and Judd–Ofelt theory, it was revealed that the highest energy transfer rate <γd5> was achieved to be 2.07 × 10−17 cm3/s for x = 0.2, and further increasing Tm2O3 content x in the fixed Yb2O3 resulted in the decrease in the energy transfer rate <γd5>. One of the plausible causes was concentration quenching of Yb3+ ions. The other was back-transfer from Tm3+ to Yb3+ ions. The influence of the condition of glass synthesis and the melting time on <γd5> was also discussed.