NaY(MoO4)(2):R (R = Sm3+/Bi3+, Tb3+/Bi3+, Sm3+/Tb3+) phosphors are synthesized by solid-state reaction method in air. The crystal structures, excitation and emission spectra, luminescence properties, the lifetimes, and the dopant concentration influences are investigated. The emission intensity of activators Sm3+ and Tb3+ can be enhanced similar to 3.04 and 1.64 times due to energy transfer (ET) from Bi3+ to Sm3+/Tb3+. NaY(MoO4)(2):Sm3+, Tb3+ phosphor with excitation 300 nm shows a tunable emission from red to yellow with change Sm3+ or Tb3+ ion concentration. Emission intensity of NaY(MoO4)(2):Sm3+ phosphor can be enhanced similar to 2.24 times via co-doping Tb3+ ion owing to ET from Tb3+ to Sm3+ ions. The results indicate that ET between sensitizer and activator (Bi3+ -> Tb3+, Bi3+ -> Sm3+, and Tb3+ -> Sm3+) is beneficial to improve the luminescence properties of activator (Sm3+ and Tb3+). ET and luminous meachanisms are explained by energy level diagrams of Bi3+, Tb3+, and Sm3+ ions.