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The Gibbs free energy of grain boundaries (GBs) in Al bicrystals has been investigated by Molecular Dynamics (MD) simulations. In our novel approach, one grain is fully embedded in a large matrix grain with fixed misorientation. Hence all inclinations are considered simultaneously since the boundary covers the full orien- tation subspace. A synthetical driving force is employed to counteract the shrinkage of the embedded grain by the capillary forces. Hence, the number of atoms of the embedded grain is kept constant, but its shape adjusts itself at elevated temperatures in order to minimize the total GB energy. The quasi-equilibrium shapes are used to derive the GB energy γ(n) as functions of the GB plane normal n. For GBs with the misorientations Σ5〈001〉 and Σ7〈111〉, analytical functions were derived and validated in a mesoscopic front-tracking simulation: the latter simulations recovered the grain shapes observed in MD simulations. For the Σ5〈001〉 misorientation it is shown that the anisotropy of γ(n) varies quite strongly with temperature. For a Σ9〈110〉 misorientation, the derived numerical energy function was found to be rather complex, showing pronounced energy minima for mixed tilt/ twist GBs parallel to {111} crystal planes.