Grain boundary (GB) structure determination at an atomic level by HREM had received increasing attention in recent years. However, models of grain boundary structure deduced from the experiment results are usually not unique, and they do not necessarily represent the equilibrium structure. A newly developed quantum-molecular-dynamics (QMD) method, which does not depend on any empirical potentials, can be used to test these models and find the equilibrium atomic structure through simulated quenching. The method employs an electronic structure tight-binding model based on density functional theory within the local density approximation and the nonlocal pseudopotential scheme, and is used to compute the total energy and atomic forces for a variety of covalent materials. In the present study, this QMD method, coupled with image simulation, was used to predict the relaxed atomic configuration for the Σ=13 (510), [001] tilt grain boundary in Si.