Based on the new ab initio molecular dynamics method by Kühne et al. [Phys. Rev. Lett. 98, 066401 (2007)10.1103/PhysRevLett.98.066401], we studied the mechanism of superionic conduction in substoichiometric Li-poor Li_{1+x}Al alloys by performing simulations at different temperatures for an overall simulation time of about 1 ns. The dynamical simulations revealed the microscopic path for the diffusion of Li vacancies. The calculated activation energy (0.11 eV) and the prefactor (D_{0} = 6.9 x 10;{-4} cm;{2}/s) for Li diffusivity via a vacancy-mediated mechanism are in good agreement with experimental NMR data. The calculation of the formation energies of different defects-Li and Al Frenkel pair and Li antisites-revealed that only Li;{+} vacancies and Li_{Al} antisites are present in the stability range of the Zintl phase -0.1 < x < 0.2.