We report for the first time, to the best of our knowledge, the quasi-three-level Nd: Lu3Al5O12 (Nd:LuAG) ceramic laser on F-4(3/2)-> I-4(9/2) transition. The dual-wavelength operation of a diode-pumped Nd:LuAG quasi-three-level laser at 941 and 946 nm was demonstrated with two intracavity Lyot filters. The output power ratio of the dual-wavelength laser could be adjusted by rotating the Lyot filter. At an absorbed pump power of 16.4 W, the total output power of the dual-wavelength laser was more than 2.36 W with 1:1 power ratio. The total slope efficiency and the optical-to-optical efficiency with respect to the absorbed pump power were more than 19.6% and 14.4%, respectively.