According to the characteristics of aluminum alloy extrusion, which means severe large deformation, thermo-dynamics coupled, and a dead zone at the front of billet, a finite volume method (FVM) based on Eulerian description was adopted to simulate the extrusion deformation of complex profile grade 3. With FVM, the traditional problems and difficulties, such as dead zone faced by rigid-plastic FEM, and grid distortion and remeshing faced by Lagrangian described finite deformation elastic-plastic FEM, can be effectively avoided. During the simulation, Eulerian described FVM is used to simulate the flow of billet, Lagrangian described FEM is used to simulate the deformation and stress of mold, and explicit dynamic contact algorithm is used to simulate the counteraction between the billet and the mold. In order to improve the efficiency of calculation, appropriate minimum size of FV grid and maximum number of FV elements are ascertained based on the good balance between the accuracy and speed of simulation. A series of thermo-constructional-frictional models are set up according to different deforming temperatures. Elaborate deformation results including exactly distributions of metal flow, stress, strain, temperature, and density in both plastic and plastic-elastic zones are obtained, which is a good base for the future optimization of process and mold parameters.