Molecular dynamics simulations were performed to analyze the curvature-driven shrinkage of individual cylindrical grains with geometrically different boundaries in Al. Grains with <100> tilt and mixed tilt-twist boundaries with the misorientations 5.5°, 16.3°, and 22.6° were simulated. The results revealed that the shrinking grains with tilt boundaries concurrently rotate increasing the misorientation angles, whereas grains with the mixed boundaries did not rotate during their shrinkage. Apparently, the grain boundary geometry/structure has a crucial impact on the observed rotational behavior of the computed grains. The grains with tilt boundaries rotate due to the lack of effectively operating mechanisms for annihilation of edge dislocations, which compose such boundaries. In contrast, for the mixed boundaries composed of edge-screw dislocations the sufficiently fast operating mechanisms of dislocation elimination are available, which facilitates grain shrinkage without rotation.