Highly correlated ab initio calculations have been performed for an accurate determination of the electronic structure and of the spectroscopy of the low lying electronic states of the ZnF system. Using effective core pseudopotentials and aug-cc-pVQZ basis sets for both atoms, the potential curves, the dipole moment functions, and the transition dipole moments between relevant electronic states have been calculated at the multireference-configuration-interaction level. The spectroscopic constants calculated for the X2Sigma + ground state are in good agreement with the most recent theoretical and experimental values. It is shown that, besides the X2Sigma + ground state, the B2Sigma +, the C2Pi , and the D2 Sigma+ states are bound. The A2Pi state, which has been mentioned in previous works, is not bound but its potential presents a shoulder in the Franck-Condon region of the X2Sigma + ground state. All of the low lying quartet states are found to be repulsive. The absorption transitions from the v=0 level of the X2Sigma + ground state toward the three bound states have been evaluated and the spectra are presented. The potential energy of the ZnF− molecular anion has been determined in the vicinity of its equilibrium geometry and the electronic affinity of ZnF EA=1.843 eV with the zero energy point correction has been calculated in agreement with the photoelectron spectroscopy experiments.