Abstract: This paper presents the symplectic scheme-matrix algorithm for solving the vibrational and vibrational-rotational energy eigenvalues of ⁷Li₂ in A¹Σ_u⁺ state, and compares the computed results with the results calculated by Ley-Koo et al.. The results show that our method is convergent and reliable, and it is a reasonable method for computing the vibrational and vibrational-rotational energy eigenvalues of diatomic molecules. Since the symplectic scheme-matrix algorithm transforms the question of the solution of the radical equation of the diatomic molecules into that of the eigenvalues of the real tridiagonal symmetric matrix, it is more simple and needs smaller computer memory and less computing time compared with the method of expanding eigenfunctions of diatomic molecules used by Ley-Koo et al.