In this talk, we will introduce a conjugate gradient method for electronic structure calculations. We propose a Hessian based step size strategy, which together with three orthogonality approaches yields three algorithms for computing the ground state energy of atomic and molecular systems. Under some mild assumptions, we prove that our algorithms converge locally. It is shown by our numerical experiments that the conjugate gradient method is efficient. This is a joint work with Zhuang Liu, Liwei Zhang, and Aihui Zhou.