Energy levels of two-electron confined in quantum ring whose height and width are considerably smaller than the interior diameter are studied. The adiabatic procedure is used in order to decouple the fast electron motion in z direction from the slow in-plane motion. A one-dimensional wave equation with periodic boundary conditions which describes the two-electron rotation around the axis and gives all low-lying two-electron levels is derived. We show that as the ring height and width tend to zero it gives the results in a good accordance with those obtained previously for the model of a one-dimensional nanoring by using a different method.