A　Finsler　metric　F　is　said　to　be　spherically　symmetric　if　the　orthogonal　group　O(n)　acts　as　isometries　of　F.　In　this　paper,　we　show　that　every　spherically　symmetric　Finsler　metric　of　isotropic　Berwald　curvature　is　a　Randers　metric.　We　also　construct　explicitly　a　lot　of　new　isotropic　Berwald　spherically　symmetric　Finsler　metrics.