The authors completely classify the Lagrangian submanifolds in complex projective space with parallel second fundamental form by an elementary geometrical method. They prove that such a Lagrangian submanifold is either totally geodesic, or the Calabi product of a point with a lower-dimensional Lagrangian submanifold with parallel second fundamental form, or the Calabi product of two lower-dimensional Lagrangian submanifold with parallel second fundamental form, or one of the standard symmetric spaces: \(SU(k)/SO(k),\) \(SU(k),\) \(SU(2k)/Sp(k) (k\geq 3),\) \(E_6/F_4.\) By using the correspondence between \(C\)-parallel Lagrangian submanifolds in Sasakian space forms and parallel Lagrangian submanifolds in complex space forms, they can also give a complete classification of all \(C\)-parallel submanifolds of \(S^{2n+1}\) equipped with standard Sasakian structure.