A thirteen-velocity three-dimensional lattice Boltzmann model on a cubic grid is presented. The transport coefficients derived from the standard Chapman-Enskog expansion are given together with the conditions for isotropy and Galilean invariance. The different invariants of the model are discussed. The results of measurements of drag and torque on a free falling sphere in a cylinder are in good agreement with solutions of the Navier-Stokes equation. Comparison of the time evolution of a freely decaying Taylor-Green vortex computed by fast Fourier transform and by the present model is presented.