A method for picosecond time‐resolved pump–probe Raman spectroscopy using temporally incoherent light (‘incoherent pump–probe Raman spectroscopy, or simply IPPR spectroscopy’) is proposed. The theoretical formulation of IPPR scattering based on Gaussian random statistics is described. It is predicted that the temporal resolution in IPPR experiment is not determined by the duration of pump and probe pulses, but by the cross‐correlation time between the pump and probe lights. The delay‐time dependence of the IPPR intensity is expected to show the same behaviour as that in conventional time‐resolved Raman spectroscopy which uses coherent ultra‐short light pulses, except for a constant background always existing in IPPR scattering. This method was examined experimentally for Raman scattering from electronically excited trans‐stilbene in n‐hexane solution. In accordance with the prediction, picosecond decay of the Raman band at 1565 cm−1 arising from the trans‐stilbene molecules in the S1, state is observed with the use of nanosecond pump and probe pulses with a cross‐correlation time of ca. 100 ps. No decay is observed for the Raman bands of the solvent. Effects of saturation arising from the frequency‐doubling, pumping and Raman processes on the IPPR signal are also discussed. The ratio of the delaytime dependent part to the background (contrast ratio) is predicted to decrease in the presence of saturation.