Abstract: The full vibrational energies of NaH and CsH molecule electronic ground states are calculated by using the variational algebraic method (VAM) established in our previous work. And then, accurate analytical potential energy function is determined by the variational algebraic energy consistent method (VAECM) with an adjustable parameter λ for each electronic state. The potential energy curves not only repeated known experimental vibrational energies well in low vibrational excited states, but also had a correct physical behavior in the region of the dissociation area, and correctly converged to the experimental dissociation energy. The results show that the VAECM analytic potential energy function is better than the research results of other methods for each electronic state in this work.