A statistical study of magnetic fluctuations near the front boundaries of magnetic clouds is approached with the method of Minimum Variance Analysis, based on the data of Imp8 and Wind spacecraft. New discoveries are that (1) fluctuation anisotropy tends to increase across the front boundaries of magnetic clouds; (2) there is a good correlation between the fluctuation anisotropy and the geomagnetic activity indices; and (3) in some cases, although there is southward field component immediately after the front boundary, Kp index descends (or Dst index ascends) with a corresponding decrease of the fluctuation anisotropy; in other cases with no distinct southward field component, Kp index ascends (or Dst index descends) with a corresponding increase of the fluctuation anisotropy. Thus we suggest that the fluctuation anisotropy might be a useful indicator in diagnosing the magnetic activities of magnetic clouds.