High-temperature solid-state reaction technique was used to prepare NaY(MoO4)2:Tb3+ phosphors with different Tb3+ concentrations. XRD patterns showed that the prepared samples contained only single-phased compound NaY(MoO4)2. The concentration-dependent green luminescent intensity of Tb3+ was studied, and it was found that the concentration quenching process is in charge of Ozawa's model. The concentration-effect of luminescence decay of 5D4 level was explained by the Auzel's self-generated quenching theory. Starting from the Reisfeld's theory, the analysis on the luminescence decays also indicated exchange interaction was responsible for the concentration quenching. Temperature dependences of the green emission intensity and decay were comprehended based on the crossover mechanism. A novel temperature sensing technique rooting in the fluorescence dynamics of 5D4 level of Tb3+ in NaY(MoO4)2 was proposed, and the absolute and relative sensitivities were deduced and assessed.