The structural and electronic properties of spinel LiMn2O4 and its Al doping system LiAl0.125Mn1.875O4 are investigated within the density functional theory in both the generalized gradient approximation (GGA) and the GGA with Hubbard U correction (GGA+U). The results from the GGA method suggest that LiMn2O4 has a cubic structure and the valences of Mn ions are all +3.5, which is unable to explain the Jahn-Teller distortions in the material. The band structure of LiMn2O4 predicted by the GGA method is also inconsistent with experimental result. With the GGA+U method, the low temperature structures of LiMn2O4 and its Al doping system LiAl0.125 Mn1.875O4 are shown to be orthogonal, the two different valence states of Mn, i.e., Mn3+/Mn4+ ions, are then determined, which is then able to explain the Jahn-Teller distortion in octahedron Mn3+O6 and the non-existence of distortion in octahedron Mn4+O6. These results are in good accordance with experimental data. Their band structures by GGA+U calculations are also consistent with experimental results. The GGA+U calculations on the LiAl0.125Mn1.875O4 indicate that with the replacement of an Mn by Al, the crystal structure and electronic properties are not significantly changed, but the Jahn-Teller distortion in octahedron Al3+O6 can be effectively eliminated, which could improve the performance of the anode materials based on LiMn2O4. The phenomenon is in consistent with the electrochemical experiments.