An irreversible character of the intramolecular vibrational energy redistribution (IVR) is discussed, and a novel definition of entropy of molecular vibration is proposed. A generalized master equation having a non-Markovian memory kernel for the occupation probability (squared modulus of the probability amplitude) is derived from the Schrodinger equation. Long-time behavior of the occupation probability is analyzed by the renormalization-group method. The occupation probability exhibits secular motion when recurrences of the memory kernel are suppressed by an exponential-damping factor e(-epsilon t). The secular motion obeys a Markovian master equation and represents quasi-irreversible dynamics, which is embedded in the reversible quantum dynamics and caused by the suppression of the recurrences. Transition rates of the quasi-irreversible dynamics are discussed in connection with molecular absorption spectra. The epsilon-dependence of the transition matrix clarifies the mechanism giving rise to the quasi-irreversibility. The irreversible character of the secular dynamics can be utilized to estimate the entropy, which indicates the extent of the IVR proceeded up to a given time.