The physical properties including the structural, electronic, mechanical, lattice dynamical and thermodynamic properties of α-LiAlO2 are investigated using first-principles calculation. It is found that α-LiAlO2 is an insulator with an indirect gap of 6.319 eV according to band structure and density of states. The elastic constants are obtained and the results indicate that α-LiAlO2 is mechanically stable. The mechanical properties including bulk modulus (B), shear modulus (G), Young’s modulus (E), Poisson’s ratio (υ) are predicted with the value of 147.0 GPa, 105.2 GPa, 254.8 GPa and 0.211, respectively. The phonon dispersion curves and the phonon density of states are also calculated. The calculated phonon frequencies for the Raman-active and the infrared-active modes considering the LO-TO splitting are assigned. The two Raman active frequencies are 407.0 cm−1 of Eg mode and 628.8 cm−1 of A1g mode, and show satisfactory agreement with experiment. The thermodynamic functions such as ΔF, ΔE, CV and S is predicted by using the phonon density of states. These results provide valuable information for further insight into the properties of α-LiAlO2 in atomic scales, which is strategically important in ITER and in molten carbonate fuel cells (MCFC).