A warm-white emitting persistent luminescence phosphor Lu_3Al_2Ga_3O_(12):Pr~(3+) was synthesized by solid state method at 1600 °C in air. The refined crystal structure of Lu_3Al_2Ga_3O_(12) host was solved by X-ray diffraction(XRD). The photoluminescence spectra, decay curve and thermoluminescence were investigated. It was revealed that the persistent luminescence originated from the f-f transitions of Pr~(3+) emitters at Lu~(3+) sites in LuO_8 polyhedrons, and it showed white color due to the ~3P_0→~3H_4, ~3P_1→~3H_5, ~3P_0→~3H_5, ~3P_0→~3H_6, ~3P_0→~3F_2, ~3P_0→~3F_3 and ~3P_0→~3F_4 transitions of Pr~(3+) emitters in a wide range. The persistent luminescence of Pr~(3+) in this host could be promoted by f-d transition(278 nm) but f-f transitions, due to the different thermal activation energy. The persistent luminescence of the optimal sample could be actually recorded for 3 h by the definition of 0.32 mcd/m~2 and was visible for more than 7 h by dark-adapted vision in darkness. The initial depth of the dominant shallow traps was calculated to be about 0.56 eV, which is suitable for persistent luminescence. The different roles of the shallow and deep traps on the persistent decay process were investigated. Accordingly, the persistent luminescence processes and mechanism of the as-synthesized Lu_3Al_2Ga_3O_(12):Pr~(3+) phosphors were proposed. A refined synthesis of Lu3Al_2Ga_3O_ (12): Pr ~ (3+) was synthesized by solid state method at 1600 ° C in air. The refined crystal structure of Lu_3Al_2Ga_3O_ (12) host was solved by X-ray diffraction It was revealed that the persistent luminescence originated from the ff transitions of Pr ~ (3+) emitters at Lu ~ (3+) sites in LuO_8 polyhedrons, and it showed white color due to the ~ 3P_0 → ~ 3H_4, ~ 3P_1 → ~ 3H_5, ~ 3P_0 → ~ 3H_5, ~ 3P_0 → ~ 3H_6, ~ 3P_0 → ~ 3F_2, ~ 3P_0 → ~ 3F_3 and ~ 3P_0 → ~ 3F_4 transitions of Pr ~ 3+) emitters in a wide range. The persistent luminescence of Pr ~ (3+) in this host could be promoted by fd transition (278 nm) but ff transitions, due to the different thermal activation energy. The persistent luminescence of the optimal sample could be actually recorded for 3 h by the definition of 0.32 mcd / m ~ 2 and was visible for more than 7 h by dark-adapted vision in darkness. The initial depth of the dominant shallow traps was calculated to be about 0.56 eV, which is suitable for persistent luminescence. The different roles of the shallow and deep traps on the persistent decay process were investigated. of the as-synthesized Lu_3Al_2Ga_3O_ (12): Pr_ (3+) phosphors were proposed.