The development of optical thermometers operating within the first biological window (650-1000 nm) has drawn great interest lately in the biological and medical fields. Here a new type of luminescent thermometer relying on the intensity ratio between G41-F43 (652 nm) and F2,33-H63(691 nm) transitions in Tm3+/Yb3+:BaMoO4 phosphor is reported under 980 nm excitation. The thermometry is found to be independent on the excitation power, benefiting the reduction of the measurement error. Moreover, it exhibits extremely high absolute sensitivity ranging from 210.5×10-4 to 1034.5×10-4 K-1 in 298-498 K. The maximal relative sensitivity and temperature resolutions (1.36% K-1 and 0.37 K, respectively) are also among the highest values of those previous thermometric materials. This Letter provides guidance in selecting the suitable emission bands to construct the ratiometric luminescent thermometers with high performance.