The relativistic pseudopotential CASSCF/CI calculation has been performed for the ground state (X1Σ+) and a few low-lying excited states (A3Π,B3Σ+,C1Π and D1Σ+) of van der Waals molecule ZnNe. The electronic structure, the potential energy curves and the spectra constants of the states have been obtained. For the ground state (X1Σ+),the equilibrium distance(Re=0.43nm) obtained in this paper is in well agreement with the corresponding experimental value (0.43nm) and the dissociation energy (De=79cm-1) is od comparing with the experimental value (23.4cm-1). For the other states (A3Π, B3Σ+, C1Π and D1Σ+), the Re is 0.425, 0.55, 0.40 and 0.55nm, respectively and the De is 74.6,unstable,232.53 and 129.45cm-1 respectively. We think that these values are reasonable comparing with those of the similar molecule such as CdNe, although the corresponding experimental values are unavailable. The potential curves show that the wells of Πstates are deeper than those of the corresponding Σ states, and the bond lengths of Π states are shorter than those of the corresponding Σ states. From the electronic structure analysis, the bonds of ZnNe for the low-lying states can be described as the static charge attractive force which stems from atomic charge transfer produced by atomic orbital overlaps as well as van der Waals′force.