The density functional theory on the level of generalized gradient approximation and full-potential linearized augmented plane wave, and the two-dimensional cubic fitting method have been used to calculate the geometrical and elastic property of LaNi3.75Al1.25 compound. The results indicate that the substitutional Al atoms in this compound are most likely to occupy part of the equivalent positions of 3g and 2c. The optimized lattice parameters a=b=0.5137 nm，c=0.4018 nm, the elastic constants C11+C12=281.2, C13=82.3, C33=227.3, the bulk modulus B＝124.5 and shear modulus G＝68.2 GPa have also been worked out. The density of state, band structure and charge density have been presented, and the electronic specific heat 23.45 mJ/molK2 for LaNi3.75Al1.25 has been estimated.