This paper proposes a method based on quaternion for characterization a helix of proteins. The method defines the parameter called Quaternion Helix Axis Spherical Distance (QHASD) on the basis of mapping protein Cα frames' helical axis onto a unit sphere, and uses QHASD to characterize the a helix of the protein secondary structure. Application of this method has been verified based on the PDBselect database, with an a helix characterization accuracy of 91.7%. This method possesses significant advantages of high detection accuracy, low computation and clear geometric significance.