In this paper we present a quantum mechanical study of the rates of vibrational predissociation of the T-shaped HeI2(B) van der Waals molecule. The van der Waals bond is characterized in terms of Morse type atom-atom interaction and by a Buckingham type atom-atom potential. The dynamics of vibrational predissociation is shown to be insensitive to the long-range part of the van der Waals potential and the Morse form is adequate for the description of this process. The close-coupling equations for nuclear motion are solved by standard numerical methods and the vibrational predissociation rates are related to the widths of the resulting resonances. The superlinear theoretical dependence of the vibrational predissociation rates on the excess vibrational energy of the molecular I2 bond is in good agreement with the experimental data. The relative contribution of intramolecular and of intermolecular terms to this superlinear dependence are elucidated, demonstrating the effects of the anharmonicity of the molecular bond on the intramolecular dynamics.