This paper aims to consider the energy-preserving finite element method (FEM) for the general nonlinear Schrödinger equation with wave operator. Optimal error estimates and superconvergence of the energy-preserving scheme are proved rigorously without any time-step restriction, which cover a general nonlinearity. There are two ingredients in our analysis. First, a temporal-spatial error splitting argument is employed to split the error into temporal error and spatial error. Second, by use of the cut-off function technique for the nonlinearity, the discrete auxiliary problems are introduced so as to verify the well-posedness of temporal semi-discrete and fully-discrete schemes, and to derive the temporal error with order O ( τ 2 ) in H 2 -norm and spatial error with order O ( τ 2 + h 2 ) in H 1 -norm, respectively. In addition, by virtue of the idea of combination between interpolation and projection, as well as the interpolated postprocessing technique, the superclose and superconvergence results of order O ( τ 2 + h 2 ) in H 1 -norm are deduced for the fully-discrete scheme. At last, two numerical examples are provided to confirm theoretical analysis. Here, h is the subdivision parameter, and τ is the time step.