We explore the use of centroid molecular dynamics (CMD) for calculating vibrational energy relaxation (VER) rate constants of high-frequency molecular vibrations in the condensed phase. We employ our recently proposed linear-response-theory-based approach to VER [Q. Shi and E. Geva, J. Chem. Phys. 118, 7562 (2003)], to obtain a new expression for the VER rate constant in terms of a correlation function that can be directly obtained from CMD simulations. We show that the new expression reduces to a centroid Landau-Teller-type formula in the golden-rule regime. Unlike previously proposed CMD-based approaches to VER, the new formula does not involve additional assumptions beyond the inherent CMD approximation. The new formula has the same form as the classical Landau-Teller formula, and quantum effects enter it in two ways: (1) The initial sampling and subsequent dynamics are governed by the centroid potential, rather than the classical potential; (2) The classical force is replaced by the corresponding centroid symbol. The application of the new method is reported for three model systems: (1) A vibrational mode coupled to a harmonic bath, with the coupling exponential in the bath coordinates; (2) A diatomic molecule coupled to a short linear chain of Helium atoms; (3) A "breathing sphere" diatomic molecule in a two-dimensional monoatomic Lennard-Jones liquid. It is confirmed that CMD is able to capture the main features of the force-force correlation function rather well, in both time and frequency domains. However, we also find that CMD is unable to accurately predict the high-frequency tail of the quantum-mechanical power spectrum of this correlation function, which limits its usefulness for calculating VER rate constants of high-frequency molecular vibrations. The predictions of CMD are compared with those obtained via the linearized-semiclassical initial-value-representation (LSC-IVR) method, which does yield accurate predictions of high-frequency VER rate constants. The reasons underlying these observations are discussed in terms of the similarities and differences between these two approaches. (C) 2003 American Institute of Physics.