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A theory of time-resolved resonance Raman scattering (RRS) from molecules is developed. The time-resolved RRS cross section is defined as a product of the time-dependent vibronic energy distribution and the scattering cross section from the single vibronic level. The theory is applied to the time-resolved RRS from vibrationally hot molecules whose vibronic distribution characterized by a canonical distribution with temperature higher than that of the heat bath relaxes to the equilibrium one in the presence of a collisional vibrational relaxation. Analytical expressions for the time-resolved RRS cross section are derived within a displaced harmonic oscillator model. It is shown that in the strong coupling case the intensities of the Stokes and anti-Stokes Raman bands in the rigorous resonance case vary inversely as the time-dependent average vibrational occupation number. Some model calculations are performed to illustrate the time-dependent intensity changes of the Raman bands.