The vibrational bound states of the He2Ne+ complex have been determined using a potential energy surface previously published by Seong et al. [J. Chem. Phys. 2004, 120, 7456]. The calculation was performed by sequential diagonalization-truncation techniques in a discrete variable representation using Radau hyper-spherical coordinates. There are 52 bound levels. The ground state has an energy of 605.3 cm(-1) above the absolute minimum and lies about half way to dissociation. The evaporation energy of one He atom is equal to 866.1 cm(-1). Only four levels have energies below the classical energy for dissociation, and all the other 48 states are bound by the zero-point energy of the HeNe+ fragment. The implications of the properties of the eigenvalue spectrum and of the corresponding wave functions on the vibrational relaxation dynamics and infrared spectra of HeNNe+ clusters is discussed.