This paper presents an optimal algorithm to compute multi-degree reduction of Said-Bézier generalized Ball curves (SBGB) with endpoints constraints in the L₂-norm. Based on the relations between Said-Bézier basis, Power basis and Jacobi basis, this paper deduces the explicit transformation matrix from SBGB basis to Jacobi basis and in reverse order. Then based on the inverse matrix of the above matrix and the orthogonality of Jacobi basis, an explicit constrained algorithm for multi-degree reduction of SBGB curves in the L₂-norm is put forward. This algorithm can be used in not only Said-Ball curve and Bézier curve but also the large class curves located between the two curves. This paper proves that the algorithm has some superiorities, including approximating optimal error of the degree reduction estimated beforehand, high order interpolation in the endpoints and multi-degree reduction in one time. Numerical examples demonstrate its validity and superiorities.