Abstract: A fluctuating-lattice Boltzmann method is used for direct numerical simulations of Brownian motion of non-spherical particles. Numerical results include mean-square velocities and velocity autocorrelation functions of elliptical and rectangular particles. It showns that equi-partition theorem applies to non-spherical particles as well and energy of each degree of freedom depends on corresponding mean-square velocity or rotational velocity. Furthermore, translational temperature of Brownian particle is identical to its rotational temperature. Finally, velocity autocorrelation function of Brownian particle decays at relative long times as~ct^-1, where coefficlent c is independent of particle shape.